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Cross-Selling Investment Products with a Win-Win Perspective in
Portfolio Optimization
Özden Gür Ali
College of Administrative Sciences and Economics, Koç University, Rumeli Feneri Yolu, Istanbul, Turkey, 34450,
[email protected]
Yalçın Akçay
College of Administrative Sciences and Economics, Koç University, Rumeli Feneri Yolu, Istanbul, Turkey, 34450,
[email protected]
Serdar Sayman
College of Administrative Sciences and Economics, Koç University, Rumeli Feneri Yolu, Istanbul, Turkey, 34450,
[email protected]
M. Hamdi Özçelik
Marketing Analytics and Optimization Manager, Yapı Kredi Bank, Levent, Istanbul, Turkey, 34330,
[email protected]
Emrah Yılmaz
Advanced Analytics Department, Emirates Integrated Telecommunications Company, Dubai, UAE
[email protected]
We propose a novel approach to cross-selling investment products that considers both the customers’ and
the bank’s interests. Our goal is to improve the risk-return profile of the customer’s portfolio and the bank’s
profitability concurrently, essentially creating a win-win situation, while deepening the relationship with
an acceptable product. Our cross-selling approach takes the customer’s status quo bias into account by
starting from the existing customer portfolio, rather than forming an efficient portfolio from scratch. We
estimate a customer’s probability of accepting a product offer with a predictive model using readily available
data. Then, we model the investment product cross-selling problem as a nonlinear mixed-integer program
which maximizes a customer’s expected return from the proposed portfolio, while ensuring that the bank’s
profitability improves by a certain factor. We implemented our methodology at the Private Banking Division
of Yapı Kredi, the fourth largest private bank in Turkey. Empirical results from this application illustrate:
(1) a traditional mean-variance portfolio optimization approach does not increase portfolio returns and
reduces overall bank profits; (2) a standard cross-selling approach increases bank profits at the expense of the
customers’ portfolio returns; (3) our win-win approach increases the expected portfolio returns of customers
without increasing their variances, while simultaneously improving bank profits substantially.
Key words : Portfolio optimization, cross-selling, win-win, predictive model, private banking
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1.
Introduction
Traditional portfolio selection approaches operate based on the assumption that customers have
specific preferences for return vis-a-vis risk. In the classical portfolio analysis of Markowitz (1952),
an investor is supposed to act in accordance with her risk preference, and existing portfolio composition should not play a role in selecting the new portfolio. However, there are psychological biases
at work that may prevent investors to switch to “theoretically optimal” portfolios. Specifically,
investors show reluctance to move away from their current portfolios (a manifestation of status quo
bias) and do not necessarily form efficient portfolios (Daniel et al. 2002). This inertia should be
taken into account when new investment options are offered to investors. On the other hand, from
an institutional perspective, offering new investment options for a portfolio is akin to cross-selling,
yet with a critical difference. The emphasis in cross-selling is earnings from the customers, whereas
in portfolio selection, the objective is improving the risk-return profile of the customers portfolio.
For instance, Bhaskar et al. (2009) present an approach for selecting the optimal list of target
customers for a cross-sell campaign of a retail bank considering the response propensity and profit
from customers. However, when the cross-selling effort includes investment options, a bank has
to consider the interdependency among the investment products in the revised portfolio and the
associated return to the customer – unlike the case of trying to sell a loan or a credit card.
In this paper, we present a cross-selling approach to investment portfolio optimization that takes
into account: (1) the interests of both the customer and the bank, and (2) the customer’s probability to accept the suggested product which is estimated with a predictive model using available
historical data. The goal is to improve the customer’s portfolio return and the bank’s profitability
concurrently, essentially creating a win-win situation, while deepening the relationship with an
acceptable product. Using “new” products is expected to help the customer move along the financial maturity spectrum and render more products acceptable in the long run (Kamakura et al.
1991). We apply the proposed approach in the context of the private banking division of a retail
bank, and evaluate the practical impact of the proposed win-win policy.
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While trying to improve a customer’s return without increasing the risk, our cross-selling
approach takes the status quo bias into account by starting from the existing portfolio of the customer, rather than forming an efficient portfolio from scratch. It is important to note that the bank
could potentially earn more if the return to the customer is not the primary objective (as typical in
cross-selling). However, such an earning will most likely be short term. For a sustainable customer
relationship and loyalty, the goal should be to make both parties better off. We present empirical
evidence that it is in fact possible to create this win-win situation. Further, we explicitly take the
customer’s probability of accepting the offer into account while choosing the win-win offer. If the
probability of acceptance is left aside, a firm would simply offer products in turn, starting from
the most profitable one; however, the bank would like to avoid such frequent solicitations (Güneş
et al. 2010).
We estimate a customer’s probability of accepting a particular product offer at a given time with
a predictive model using readily available data. This analysis provides objective estimates that can
be easily/systematically updated, and allows the bank to standardize the cross-selling process. A
crucial element of the predictive model is the input information set. Our extensive experiments with
potential information sets reveal that the customer’s past product experience and recent product
returns alone provide almost as high an accuracy as using all variables. The customer’s past product
experience reflects her current financial maturity and preferences, while the recent product returns
capture the dynamic financial environment as well as the dynamic product characteristics. We also
find that demographics, current product holdings, or economic indicators do not further improve
predictive accuracy in this context.
We next give a brief review of the related literature. Importance of behavioral theory for finance
has long been recognized. For instance, Kahneman and Riepe (1998) present several biases relevant
to investor psychology, and offer recommendations to investors and financial advisors. Similarly,
behavioral elements have been introduced to the portfolio selection problem. For example, Boyle
et al. (2012) presents a framework based on ambiguity aversion to capture a customer’s familiarity
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with the asset (see also Maenhout 2004; Garlappi et al. 2007 etc.). Shefrin and Statman (1985)
and Das et al. (2010) develop portfolio optimization approaches that include mental accounting
elements (see Kahneman and Tversky 1979; Thaler 1985). Others have introduced suitability of the
asset to the customer by way of psychographic elements. For instance Gupta et al. (2010) considers
the impersonal characteristics of financial assets and psychographic profiles of the customers (based
on a survey), and identifies portfolios based on suitability and optimality. A common aspect of
these applications is that although some form of portfolio return maximization is considered, the
bank’s profits are not taken into account. We specifically address this gap in the literature.
This study is also related to cross-selling in the context of financial products. Bhaskar et al.
(2009) constructs models for customers’ likelihood of accepting an offer to determine best targets
for a specific financial product. Cohen (2004) uses similar models to identify products to be offered
to a particular group of customers. Li et al. (2011) uses a hidden Markov model to capture customer
response to cross-sell solicitations which essentially change the speed of movement between the
customer’s financial states. In their approach, short term profitability can be traded off for potentially higher long term profitability, since offers that facilitate the customers’ financial maturity
subsequently increase long run profitability. Although we do not explicitly focus on long term profitability, we consider the customer’s portfolio return, which forms the basis for customer retention
in the long run; we offer new acceptable products to the customer, which increases her financial
maturity, and deepens her relationship with the bank. In the aforementioned cross-selling studies,
the emphasis is on the profits of the bank. We complement this line of research by specifically
taking into account the customer’s risk-return trade offs in our cross-selling model, in addition to
the bank profit and customer propensity considerations.
In summary, the main contribution of our work is to present an optimization-based methodology that considers both the bank’s profits and the customer’s return in cross-selling investment
products, and incorporates a predictive model of customer’s acceptance of the product offer. We
substantiate our methodology with empirical findings from an application at the private banking
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division of a large Turkish bank, and show that both the bank and customers can potentially win
with our approach.
The rest of this paper is organized as follows. Section 2 introduces our cross-selling model to
create a win-win situation in the portfolio selection context, and describes the predictive model
for acceptance probabilities. Section 3 presents the application of our methodology in a private
banking context at Yapı Kredi Bank, the fourth largest private bank in Turkey. We also report
the results from our extensive experiments for selecting the best information sets, compare our
win-win approach to alternative benchmark policies, and present some robustness results. Section 4
discusses the real life benefits of our methodology at Yapı Kredi. Finally, we present our concluding
remarks in Section 5.
2.
Methodology
In this section, we first present a traditional approach to portfolio optimization, discuss its limitations in the banking context, and propose a cross-selling approach which improves the customers’
and the bank’s objectives simultaneously, creating a win-win situation.
2.1. A Classical Approach to Portfolio Optimization
Suppose that the bank offers an assortment of n investment products (financial instruments) which
are associated with potential returns to investors over time. We note that investment products
exclude typical retail banking products such as transactional and savings accounts, debit, ATM
and credit cards, and loans. Let N be the set of all investment products offered by the bank, i.e.,
N = {1, 2, . . . , n}. Also, let rit and σit denote the expected value and standard deviation of returns
for each product i ∈ N in period t, respectively, and σijt be the covariance between the returns of
any two products i and j in period t. These summary measures essentially quantify the risk-return
performance of the products within the mean-variance framework. Then, for a given customer, we
can express the mean return of her portfolio consisting of the bank’s n products in period t as
X
wit rit
(1)
Rt (wt ) =
i∈N
and the variance of her portfolio return as
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Vt (wt ) =
XX
k k
wit
wjt σijt ,
(2)
i∈N j∈N
where wit is the weight of product i in the customer’s portfolio in period t, ∀i ∈ N , and wt =
(w1t , w2t , . . . , wnt ). A simple approach for optimal portfolio selection in modern portfolio theory
(MPT) is to choose the weights of the products so as to maximize the expected portfolio return
by limiting the portfolio variance. This approach can be formulated as follows
max Rt (wt )
(3)
s.t.
Vt (wt ) ≤ σ 2
X
wit = 1
(4)
(5)
i∈N
wit ≥ 0, i = 1, 2, ..., n
(6)
Solving this model while systematically varying σ 2 (upper bound on portfolio variance) yields
the set of portfolios with the best risk-return combinations for different levels of risk – what is
known as efficient portfolios. MPT assumes that the customer would choose an efficient portfolio
based on her own set of risk-return indifference curves. Although (3)-(6) do not specifically consider
the customer’s utility function, Sharpe (2007) shows that this analysis would be equivalent to
maximizing a quadratic utility of portfolio returns.
This classical approach has two important characteristics relevant to our work. First, the customer’s existing portfolio does not factor into the selection of optimal portfolio. This formulation
handles the problem as if the optimal portfolio is formed from scratch, and assumes that the customer would not hesitate to move to the optimal portfolio. However, it is no trivial matter to
convince customers to move away from their existing portfolios. For one, they tend to invest in
familiar products, as unfamiliar ones are perceived as being more risky and hence less attractive
(see Daniel et al. 2002). Perhaps more importantly, there is evidence that investors exhibit status
quo bias, defined as a biased preference for the current state or option (Samuelson and Zeckhauser
1988). For instance, an option is more likely to be chosen when it is the default in a savings plan
(Madrian and Shea 2001); or investment decisions depend on the initial composition of an inherited
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portfolio (Samuelson and Zeckhauser 1988). Economic rationalization, such as the existence of a
transaction cost, does not adequately explain the status quo bias. One psychological explanation
offered is loss aversion: according to the Prospect Theory, losses and gains are compared to a
reference (status quo), and losses loom larger than commensurate gains (Kahneman and Tversky
1979). Hence potential gains should be significantly larger than losses to take an action (Kahneman
et al. 1991), which biases the decision maker to stick to the status quo. A related explanation is
the commission bias ; negative results due to an action hurt more than negative results due to
inaction (Spranca et al. 1991). In this context, any loss after a portfolio change would be perceived
as worse compared to a loss from an existing portfolio. Samuelson and Zeckhauser (1988) argue
that anchoring and insufficient adjustment is also relevant to status quo bias. When individuals are
choosing a value for a decision variable (such as the optimal investment), they take the initial value
as the starting point and adjust it considering the specifics of the problem; but the adjustment
is typically insufficient. In the end, status quo bias is associated with a tendency to hold on to
the current portfolio in our context, and might prevent the customer from making major changes
to her portfolio. Therefore, it is important that a proposed portfolio should be only marginally
different from the current one. This is consistent with the insight offered by Paolacci et al. (2011);
they demonstrate that individuals are more likely to consider an immediate alternative (which is
similar to the current endowment on some characteristics) than a more distant one.
Secondly, the classical approach ignores the role and considerations of the bank in the portfolio
selection problem. In practice, it is often the bank that offers investment alternatives to the customer. One can expect that the bank would encourage a customer to make changes to her current
portfolio if these changes both bring a better combination of risk and return for the customer, and
mean more profits for the bank itself.
The current paper proposes a new cross-selling approach for the portfolio selection problem. In
our approach, the bank would like to create a win-win situation by improving its customers’ portfolios as well as its own profitability by offering a new product to be included in the existing portfolio
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Figure 1
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Overview of key problem dimensions captured by the proposed methodology
of a customer. Figure 1 compares the classical portfolio optimization, traditional cross-selling, and
the proposed approach in terms of whether they address the three key problem dimensions, namely
the customer’s portfolio return, the acceptability of the proposed offer, and the profitability of the
bank. It is possible that our approach offers a product that is more likely to be accepted by the
customer, even though another product leads to a better risk-return combination. Clearly, taking
into account the propensity to accept is important in this context, because it might be difficult for
the bank to make another offer if one offer is refused, not only because frequent solicitations are
not desirable, but also the customer may start questioning the credibility of these offers. For this
purpose, we construct a predictive model for the customer’s propensity to add a “new” product
to her portfolio by using available data. This approach ensures objective estimates that can be
updated systematically as new information is obtained about the customer, the product, or the
environment. Thus, we capture the dynamics of customer behavior due to evolving financial maturity or environmental conditions. While customer and/or customer representative surveys have
been used to develop rules to identify the products that are admissible for a particular customer
(e.g. Gupta et al. 2010), our approach ensures that probability estimates can be obtained even
for customers who do not have the time or interest in completing surveys. Further, the predictive modeling approach does not provide room for strategic behavior that may taint a survey. We
should mention that predictive accuracy is a key component of our methodology. Accordingly, we
determine these sets that provide the best predictive accuracy by an experiment that involves a
large number of products, customers and time periods.
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2.2.
9
Win-Win Model for Cross-Selling Investment Products
Assume that the weight of product i ∈ N in the existing portfolio of a given customer in period
t is wit , and wt = (w1t , w2t , . . . , wnt ). Further, Pt ⊆ N represents the set of products in her period
t portfolio , i.e., Pt = {i : wit > 0, i ∈ N }. Then, the mean and variance of the existing portfolio
return in period t follow as
Rt (wt ) =
X
wit rit
(7)
wit wjt σijt ,
(8)
i∈Pt
and
Vt (wt ) =
XX
i∈Pt j∈Pt
respectively. Further, the bank’s percentage profit from the existing portfolio of the customer is
X
wit πi
(9)
Πt (wt ) =
i∈Pt
where πi is the percentage profit of the bank from a customer that has product i in her portfolio,
for all i ∈ N . Equation (9) implicitly assumes that the bank earns a product-specific management
fee in period t as a percentage of the customer’s investment in each product.
Now suppose the bank makes a cross-sell offer to the customer. Although the bank would prefer
to liberally adjust the customer portfolio to improve profitability and return, status quo bias implies
customer resistance to significant changes. We acknowledge this customer inertia in our model and
let the cross-sell modify the portfolio only minimally. Accordingly, the bank offers only a single
product, and limits the weight of the new product in the proposed portfolio. Moreover, we assume
that the customer does not bring additional money to the bank in response to the product offer,
i.e., the total investment amount (portfolio size) is kept the same. Further, we do not optimize
the weights of the existing products, i.e., their relative weights are held constant in the proposed
portfolio. Though consistent with the status quo bias, we note that this is indeed a special case.
These aforementioned features of our setup not only recognize the status quo bias, but also help
us disentangle the impact of our win-win approach from the potential performance improvements
due to additional investments and rebalancing of the customer’s existing portfolio.
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The bank makes a single product offer to the customer for period t + 1; the new product is not
in the customer’s portfolio in period t. If the customer accepts the offer, the number of products
in her portfolio will increase by one in period t + 1. Based on our model assumptions, the weight
of an existing product j essentially shrinks to wj,t+1 = (1 − yi )wjt , ∀j ∈ Pt , where yi is the weight
of the new product i ∈
/ Pt . Accordingly, vector wt+1 captures the bank’s offer to the customer in
period t. Noting that yi will be positive only for a single new product i ∈
/ Pt (since the bank offers
a single product at a time), we can express the mean return of the proposed portfolio in period
t + 1 as
Rt+1 (wt+1 ) =
X
j∈Pt+1
wj,t+1 rj,t+1 =
X
i∈P
/ t
(
yi ri,t+1 +
X
j∈Pt
w jt (1 − yi )rj,t+1
)
(10)
Substituting (7) in (10) yields
Rt+1 (wt+1 ) = Rt+1 (wt ) +
X
i∈P
/ t
yi (ri,t+1 − Rt+1 (wt ))
(11)
Rt+1 (wt+1 ) given in (11) is the mean return of customer portfolio in period t + 1, conditioned
on her acceptance of the bank’s proposal, and Rt+1 (wt ) is the mean return if she declines the
proposal and keeps her portfolio intact from period t to period t + 1 (essentially using wt in period
t + 1). We note that Rt (wt ) is not necessarily the same as Rt+1 (wt ), since expected product returns
could possibly change from period t to t + 1 although the customer’s portfolio composition remains
unchanged.
Let θit be the probability that the customer accepts product i if it is recommended by the bank
in period t. We discuss how to compute customer-specific θit using predictive models in detail in
Section 2.4. We calculate R̃t+1 (wt+1 ), the expected portfolio return in period t + 1 for a customer
prior to her decision on whether or not to accept the offer for product i, as
(
!
)
X
X
R̃t+1 (wt+1 ) =
θit yi ri,t+1 +
w j,t+1 rj,t+1 + (1 − θit )Rt+1 (wt )
i∈P
/ t
(12)
j∈Pt
Using (7), we simplify (12) as
R̃t+1 (wt+1 ) = Rt+1 (wt ) +
X
i∈P
/ t
yi θit (ri,t+1 − Rt+1 (wt ))
(13)
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On the other hand, we can write the variance of the proposed portfolio return in period t + 1 as
Vt+1 (wt+1 ) =
X
X
(14)
wi,t+1 wj,t+1 σij,t+1
i∈Pt+1 j∈Pt+1
=
X
i∈P
/ t
(
2
yi2 σi,t+1
+
X
j∈Pt
yi wjt (1 − yi )σij,t+1 +
XX
j∈Pt `∈Pt
(1 − yi )2 wjt w`t σj`,t+1
)
(15)
Substituting (8) in (15), we get
Vt+1 (wt+1 ) = Vt+1 (wt ) +
X
i∈P
/ t
(
2
yi2 (σi,t+1
− Vt+1 (wt )) +
X
j∈Pt
)
yi wjt (1 − yi )σij,t+1
(16)
In (16), Vt+1 (wt+1 ) denotes the variance of the customer’s portfolio return in period t + 1 if she
accepts the bank’s offer, whereas Vt+1 (wt ) denotes the variance in period t + 1 if she rejects the offer
and keeps using portfolio weights wt in period t + 1. Note that Vt+1 (wt ) could be different than
Vt (wt ) even though the customer uses the same portfolio in periods t and t + 1, because product
covariances might change in the mean time.
We express the bank profit from the particular customer in period t + 1, if the customer decides
to accept the bank’s offer and adopts the proposed portfolio, as
(
)
X
X
X
Πt+1 (wt+1 ) =
wi,t+1 πi =
yi πi +
wjt (1 − yi )πj
i∈Pt+1
(17)
j∈Pt
i∈P
/ t
We assume that product profitability (πi ) does not vary over time, i.e., Π t+1 (wt ) = Πt (wt ). Thus,
bank profitability from a given customer remains the same unless the customer changes her portfolio. Recognizing this fact and using (9), we simplify the above expression as
Πt+1 (wt+1 ) = Πt (wt ) +
X
i∈P
/ t
yi (πi − Πt (wt ))
(18)
In what follows, we model the bank’s portfolio selection problem for any given customer using a
mixed-integer nonlinear programming formulation, so as to establish a win-win outcome for both
the customer and the bank. We refer to this particular formulation as [ww].
[ww]
max R̃t+1 (wt+1 )
(19)
s.t.
wj,t+1 = (1 −
X
∀i∈P
/ t
yi )wjt ,
∀j ∈ P t
(20)
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wi,t+1 = yi ,
/ Pt
∀i ∈
(21)
Rt+1 (wt+1 ) ≥ Rt+1 (wt )
(22)
Vt+1 (wt+1 ) ≤ Vt+1 (wt )
(23)
Πt+1 (wt+1 ) ≥ (1 + Δπ)Πt (wt )
X
ˉ
yi ≤ Ω
(24)
i∈P
/ t
X
zi = 1
i∈P
/ t
(25)
(26)
yi ≤ zi , ∀i ∈
/ Pt
(27)
/ Pt
yi ≥ 0, ∀i ∈
(28)
/ Pt
zi ∈ {0, 1}, ∀i ∈
(29)
/ Pt , where zi indicates whether
The decision variables in the above formulation are zi and yi , ∀i ∈
the bank chooses to offer product i to the customer in period t, and yi is the weight of product
∗
i in the proposed portfolio for period t + 1. We denote the optimal solution to [ww] as wt+1
and
∗
). If no feasible
the optimal expected portfolio return for the customer in period t + 1 as R̃t+1 (wt+1
solution exists for [ww], the customer does not receive an offer from the bank in that period, and
∗
we simply assume that she carries her current portfolio to the next time period, i.e. wt+1
= wt ,
∗
and subsequently expects a return of R̃t+1 (wt+1
) = Rt+1 (wt ).
The objective function of [ww], given in (19), maximizes R̃t+1 (wt+1 ), the expected return of the
customer portfolio in period t + 1 prior to her acceptance/rejection decision regarding the bank’s
offer in period t. Note that R̃t+1 (wt+1 ) takes into consideration the probability that the customer
actually accepts the bank’s offer, as we define in (13). Therefore, it measures the potential impact
of the bank’s offer on the customer’s portfolio more realistically, compared to Rt+1 (wt+1 ), her
expected return as if she accepts the offer. On the other hand, the classical approach in MPT uses
Rt+1 (wt+1 ) as its objective function in (3), disregarding the acceptability of the bank’s proposal
by the customer, and offering products that might possibly be rejected.
We now discuss the constraints of [ww]. The first two constraints, (20) and (21), carry the
portfolio weights from period t to t + 1, taking into account the weight of the newly introduced
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product. The constraint given in (22) makes sure that the bank does not propose a portfolio with
a lower return than that of the existing portfolio of the customer. The constraint given in (23)
forces an upper limit on the variance of the proposed portfolio return. Essentially, the bank offers
a new product such that the risk of the proposed portfolio is not higher than that of the existing
portfolio. On the other hand, the traditional approach provided in the previous section ignores the
risk-return profile of the existing portfolio.
One of the main features of our method is the consideration given to the bank’s profitability
in the portfolio selection problem. Constraint (24) ensures that the bank’s percentage profit from
the proposed portfolio is larger than what it makes from the existing portfolio of the customer by
a certain factor, captured through the parameter Δπ, the lower limit on the desired percentage
increase in the bank’s profit level. One can also notice the relevance of this particular constraint to
the -constraint method in multi-criteria optimization (Chankong and Haimes 1983). Our win-win
model can be viewed as an optimization problem with two objectives – maximizing the customer’s
portfolio return and maximizing the bank’s profitability. Hence, we are essentially keeping the
portfolio return objective, as in (19), and using the bank profitability as a constraint bounded by
some allowable level in (24) to find a Pareto optimal solution.
The rest of the constraints in [ww] are bounds on the values of the decision variables. The bank
ˉ in constraint
limits the weight of the new product in the proposed portfolio to a maximum of Ω
(25), in order not to modify the existing portfolio of the customer significantly. This constraint is
closely related to the status-quo bias: the new portfolio should be close to the existing portfolio
of the customer. Constraint (26) forces the bank to offer only a single product at a time, while
constraint (27) sets the weight of products which are not included in the proposed portfolio to zero.
Finally, constraints (28) and (29) are the typical non-negativity and binary definition constraints.
2.3.
Measuring Performance
Suppose that the bank has m customers in period t, and let M denote the set of all customers.
We introduce three performance measures, Δ R̃, ΔΠ̃ and ΔΠ̃t , to evaluate the overall impact of
our approach on customer returns and bank profitability. Specifically, Δ R̃ calculates the expected
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percentage change in portfolio returns averaged over all customers, and ΔΠ̃ calculates the expected
percentage change in bank profitability per customer averaged over all customers. Thus, we have
n
o
P
k
k∗
k
k
R̃
(w
)
R
(w
)
−
t+1
t+1
t+1
t
k∈M
P
ΔR̃ =
(30)
× 100%
k
k
k∈M Rt+1 (wt )
and
ΔΠ̃ =
P
k∈M
n
o
k∗
Π̃kt+1 (wt+1
) − Πkt+1 (wtk )
P
× 100%,
k
k
k∈M Πt+1 (wt )
(31)
where the index k refers to a particular customer k in set M, and the notation with superscript k
indicates the variable values belonging to customer k. Moreover, we define
n o
P
k
k
k∗
k
k
S
(w
)
Π
(w
)
Π̃
−
t+1
t
t+1
t+1
t
k∈M
P
ΔΠ̃t =
× 100%,
k k
k
k∈M St Πt+1 (wt )
(32)
where Stk is the size of customer k’s portfolio in period t. ΔΠ̃t estimates the impact of our approach
on the total bank profits, and reflects the fact that customer portfolios have different sizes. Note
that all three measures take product acceptability into account. We also denote the number of
customers (out of m customers of the bank) with feasible solutions to [ww] with m∗ .
ˉ are two key operational levers of our win-win model and
We should highlight that Δπ and Ω
their values are set by the bank in line with its strategic objectives. The following two lemmas state
k
k
k
ˉ on the performance of our model, as measured by R̃t+1
the impact of Δπ and Ω
(wt+1
), Π̃kt+1 (wt+1
),
∗
m∗ and ΔR̃.
ˉ
Lemma 1. Impact of allowable change to portfolio weights (Ω):
k
k∗
ˉ
(wt+1
) is non-decreasing in Ω.
(i ) R̃t+1
ˉ
(ii ) m∗ is non-decreasing in Ω.
ˉ
(iii ) ΔR̃ is non-decreasing Ω.
Lemma 2. Impact of minimum desired change in profitability (Δπ):
∗
k
k
(i ) R̃t+1
(wt+1
) is non-increasing in Δπ.
∗
k
(ii ) Π̃kt+1 (wt+1
) is non-decreasing in Δπ.
(iii ) m∗ is non-increasing in Δπ.
∗
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(iv ) ΔR̃ is non-increasing Δπ.
ˉ increases, the feasible region for [ww]k gets larger,
Lemma 1 and 2 follow from the fact that as Ω
i.e., constraint (25) becomes looser, while as Δπ increases, the feasible region shrinks, i.e., constraint
(24) becomes tighter. Consequently, for a given customer k, her optimal expected portfolio return
k
k∗
ˉ and non-increasing Δπ. Clearly, due to the aforementioned
(wt+1
) is non-decreasing in Ω,
R̃t+1
ˉ and non-increasing Δπ. Although the
changes to the feasible region, m∗ is also non-decreasing in Ω,
likelihood that a customer receives an offer gets smaller with Δπ, the profitability of the bank from
∗
k
a customer with an offer (in the expense of customer’s portfolio return) increases, i.e., Π̃kt+1 (wt+1
)
∗
k
) = Πkt+1 (wtk ) for customers without
is increasing in Δπ. On the other hand, we have Π̃kt+1 (wt+1
∗
∗
k
k
offers, i.e., Π̃kt+1 (wt+1
) does not change with Δπ. Hence, overall Π̃kt+1 (wt+1
) is non-decreasing in
Δπ. Finally, parts (i) and (ii) imply part (iii) of Lemma 1, and parts (i) and (iii) imply part (iv)
of Lemma 2.
ˉ on Π̃kt+1 (wk∗ ) and ΔΠ̃ is not clear and depends on profitability and
Note that the impact of Ω
t+1
∗
k
return characteristics of the bank’s products. Although increasing Δπ increases Π̃kt+1 (wt+1
) for
those customers with offers (Lemma 2(ii)), since m∗ becomes smaller with Δπ (Lemma 2(iii)), a
larger Δπ does not readily translate to larger per customer profitability for the bank. In Section
3.3, we present our empirical results regarding the overall impact of these two operational levers
on customer returns as well as bank profitability.
2.4.
Predictive Model for Acceptance Probabilities
We define θit as the probability that a given customer adds product i to her portfolio in the next
period t + 1 in response to the bank’s offer, given that product i is not in her portfolio in period t.
We refer to θit as the customer’s acceptance probability of product i in period t. Let
θit = f (pit )
(33)
where pit is the corresponding probability when she makes the same decision without an offer from
the bank, presumably using her own discretion, and f (.) is a function linking pit to θit . Hereafter,
we refer to pit as the customer’s adoption probability of product i in period t. We expect θit to
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be higher than pit , and postulate that f (.) is increasing in pit , depending on the effectiveness of
the bank’s cross-selling efforts. This is consistent with the empirical evidence from Li et al. (2011)
which report that a cross-selling solicitation of a given product positively impacts the customer’s
purchase probability of the product. At a conceptual level, a cross-selling offer should increase
awareness and interest for the product, similar to that in advertising (Mehta et al. 2008), thereby
resulting in an increased likelihood of purchase.
We empirically model the probability pit that the customer will adopt product i in t + 1, using
available data. The customer may keep the same portfolio, or add several products to the current
portfolio in the next period. Therefore, the probabilities pit across products for a customer do not
have to add up to 1. We estimate pit with product-specific binary logistic regression models, which
predict the log odds of pit with a linear function of the vector of predictor variables xit whose value
is known at time t:
pit
ln
1 − pit
= αi + βi xit + it
(34)
We choose logistic regression for the following reasons. First, it is relatively simple, and lends
itself easily to interpretation. Hence, it is widely used for modeling choice both in academia and
industry (Kim et al. 2005). Second, in the context of financial product choice, evolving customer
financial maturity, and time dependent environmental effects such as economic conditions and
product performance, there is evidence that the predictive accuracy of the customer’s product
choice does not increase significantly with more sophisticated methods; rather, accuracy depends
heavily on the input variables (Knott et al. 2002, Moon and Russell 2008). Third, adding a product
to their portfolios is a rare event for many customers, particularly for products that are offered to
a relatively small core group of more sophisticated customers (a general trait of private banking
customers). Methods that do not partition the data, such as logistic regression, are preferred over
divide-and-conquer type methods, such as decision trees, when predicting such rare events (Weiss
2004).
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As explained earlier, the predictive accuracy of the models are sensitive to the input information
set. Therefore, we conduct extensive experiments to measure the contribution of different information sets to the accuracy of next product prediction and to select the information sets to be
used. We present the results of these experiments, using data from the private banking division
of Yapı Kredi Bank, in Section 3.2. The individual logistic regression models further select the
variables out of the relevant information set using the stepwise routine.
3.
Application
In this section, we present the case study involving the Private Banking Division of Yapı Kredi for
the above proposed methodology. Our goals are two-fold: First, we provide simple and accurate
models to predict the likelihood that the private banking customer will adopt a product of interest.
For this purpose, we run extensive experiments using customer demographics, transactions, product
and environmental data. Second, using the results from our predictive model, we illustrate the
potential impact of the win-win model on the bank profitability as well as the customers’ returns.
Specifically, we explore the following research questions: 1) What are the information sets that
provide an accurate and simple model for predicting the customer’s product adoption probability?
2) Does the proposed win-win model yield beneficial results for both the bank and the customers in
a real setting? 3) What is the added value of considering customer acceptance probabilities for the
customer and the bank? 4) What is the impact of key operational levers on the effectiveness of the
proposed approach?
Next, we introduce the case study setting, then describe the experiments we conduct to identify
the smallest information sets that provide the best accuracy for product adoption probability
prediction, followed by results from our cross-selling application.
3.1.
Setting
Yapı Kredi is the fourth largest private bank in Turkey with 10.6 million customers and approximately 89 billion US Dollars in assets. Its private banking division, Yapı Kredi Private Banking
(hereafter referred to as ykpb), serves high net worth individuals, with personal financial assets
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over 280 thousand US Dollars. The term private refers to customer service (ranging from personal
financial services to unique advisory services in art, philanthropy, tax, retirement, insurance, inheritance, etc.) delivered to these customers on a more personal basis than in a typical retail banking,
usually via dedicated bank advisers, called Relationship Managers (rm) at Yapı Kredi.
Although many investment products (41 products) are offered by the bank, such as mutual
funds, bills and bonds, fund deposits, etc., private banking customers traditionally prefer short
term fixed deposits. More specifically, while fixed deposit products are used by a large majority,
many products are used by less than 1% of the existing customer body. Declining real interest
rates, during Turkey’s transition from double digit to single digit inflation, presents an opportunity
for the bank to introduce customers to these other products. However, customers are reluctant to
adopt “new” products readily, since in the past they had enjoyed relatively high real returns.
In addition to different risk-and-return characteristics presented by alternative investment products, profit margins for ykpb also vary across products. For instance, for highly commoditized
products, such as fixed deposits, profitability tends to be relatively low, and for products where
the bank has a competitive advantage, it tends to be higher. Therefore, choosing the product to
propose to a customer involves trade-offs in terms of profitability. The challenge for ykpb is to
implement a systematic approach in offering investment alternatives to customers, while improving
its own profitability and customers’ portfolio returns at the same time.
We should note that ykpb does not manage its customer portfolios on their behalf. In other
words, ykpb does not perform “Portfolio Management”, but rather informs customers about the
changes in the market and only makes general investment suggestions. Effectively, portfolios are
under the direct control of customers – customers use their own discretion to accept or reject any
offers from the bank. From ykpb’s perspective, offering new investment options for a portfolio can
be seen as a cross-selling effort.
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Our dataset includes monthly account activities of 7,021 customers between June 2008 and
October 20101 . In the first stage of our application, we use this dataset in addition to relevant
data about product returns and economic indicators, to subsequently estimate the probability
of acceptance of each product by each customer if an offer is made in October 2010. Then, in
the second stage, we solve the win-win model for each customer incorporating these estimated
probabilities, and propose new portfolios for November 2010.
As a management strategy, ykpb avoids one-time fees (transaction fees) as they believe that these
will have a negative impact on the satisfaction of their high value customers. This is in contrast with
other contexts (e.g. retail banking, brokerage), in which transaction fees might indeed account for a
significant income. For mutual funds, ykpb charges a certain percentage of the investment amount
as management fee every month. In some other products, such as fixed deposits, the bank profits
from the spread between the interest rate paid to the investor and the rate collected from credits.
Hence, ykpb’s per period profits from a customer portfolio can be expressed as a percentage of
her investment in each product.
Figure 2 depicts the risk – as measured by standard deviation – as a function of expected return
in November 2010, for products in various asset classes, Figure 3 illustrates the bank’s profitability
from each product as a function of its expected return 2 , and Figure 4 shows profitability as a
function of risk-adjusted returns (Sharpe ratios). Not surprisingly, we observe that products with
high expected returns have high risks. On the other hand, not all products with high expected
returns bring high profits to the bank. This observation applies to risk-adjusted returns as well.
We note that although the interests of the bank and the customers are not naturally aligned, there
is still room for constructing win-win portfolios in this particular setting.
1
Although the study period overlaps with the financial crisis of 2008, the impact of this crisis on Turkish economy
was limited. While S&P 500 depreciated 32.7% between June 2008 to June 2009 (overlap of the crisis with the study
period), the local stock exchange index depreciated only 10.3%.
2
We use simple averages to estimate expected product returns.
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Bank Profitability
Standard Deviation
20
E x p ec ted R etu rn
Figure 2
E x p e c te d R e tu rn
Figure 3
Product return standard deviation as a
expected return
Bank Profitability
function of expected return
Bank profitability as a function of
C om m od ity
E q u itie s
F ix e d inc om e
M one y m arke t
A lte rnativ e p rod u c ts
S h arp e R atio
Figure 4
Bank profitability as a function of
Sharpe ratio
3.2.
Estimating Acceptance Probabilities
In this section, we specify θit , the probability that a particular customer accepts the bank’s offer,
given that the offered product is currently not in her portfolio. First, we select the information sets
to be used in product-specific logistic regression models for the customer’s adoption probability pit
of product i in period t. Then using these information sets, we predict pit (predicted values are
denoted by p̂it ) for all products that the customer does not have in her portfolio as of October
2010.
The function f (.) given in (33) accounts for the impact of cross-selling – acceptance when the
product is offered by the bank versus adoption without an offer. Indeed, the offer acceptance
probability is (likely to be) higher than the adoption probability; nevertheless, to the best of our
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knowledge, extant literature does not provide any empirical or analytical insights regarding the
form of f (.). In this application, we assume a simple piecewise linear form for f (.) and limit the
maximum value of θit to 1. Hence, we specify θit as follows
θit = f (p̂it ) = min {1, Φ ∙ p̂it }
(35)
where Φ is a constant. We examine the sensitivity of the performance of our methodology to the
mapping function in terms of the parameter of the assumed piecewise linear function, i.e., the
multiplicative factor Φ (in Section 3.3), as well as the functional form (in Section 3.4).
3.2.1.
Selecting Information Sets for the Predictive Model. The cross-selling problem
has been associated with offering the right product to the right customer at the right time (Li
et al. 2011). If one assumes that the investment product characteristics are static over time, the
most important variable affecting the customer’s decision over time is the customer – her demographics, and how she views the available products. Under this assumption, as the customer’s
financial maturity increases, she is ready to purchase more sophisticated products. It is possible
to infer the customer’s financial maturity from the products that she has previously used, and
then utilize this information to explain and predict subsequent product use (e.g. Moon and Russell
2008; Li et al. 2005; and Prinzie and Van den Poel 2006). Some papers exploit the customer’s
current financial product information to predict the next product (Knott et al. 2002), which may
be particularly valuable in a product portfolio optimization context. On the other hand, important product characteristics, such as relative return, actually vary with economic conditions. For
example, investors tend to buy t-bills and gold more heavily when the state of the economy is
not promising, while stocks become more attractive when the economic conditions are expected to
improve. Hence, investigating the right time may have to consider the current economic conditions
and recent investment product performances.
For these reasons, we investigate the predictive power of the following information sets and
identify the smallest subset providing highest accuracy in predicting the customer’s adoption of a
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certain product. 1) Current-Use (41 binary variables): Current-Use i = 1 if Product i is present in
the customer’s current portfolio; 0 otherwise. 2) Ever-Used (41 binary variables): Ever-Used i = 1 if
Product i was ever present in the customer’s previous portfolios; 0 otherwise. 3) Demographics (10
variables such as age, gender, education, etc.) 4) Economic Indicators (10 variables including indices
for consumer confidence, stock markets, interest and exchange rates) 5) Returns 3 (30 variables):
percentage returns for the current month capture two phenomena: (i) Customers’ reactions to the
recent performance of the focal product, which may be a positive feedback behavior (e.g. DeLong
et al. 1988) or a contrarian behavior (e.g. Goetzmann and Kumar 2008); (ii) Current effect of the
economic conditions on the performance of the bank’s alternative products. To the best of our
knowledge, neither of the last two groups (Returns and Economic Indicators ) has been explicitly
considered in existing literature as a driver or influencer of the financial product choice in crossselling models.
We conduct an experiment to identify which of the five information sets to include in stepwise
logistic regression models. Our focus here is the predictive accuracy of the model; thus we set
aside a randomly selected holdout sample (10% of customers) for evaluating the model accuracy.
Specifically, we examine models using: (1) variables from a single information set at a time (five
models), (2) variables from two information sets at a time (ten models), (3) variables from all
information sets (one model).
For our experiments, we coded the available customer-specific transactions data as follows: Positive instances refer to events where a customer does not have product i in the portfolio in period
t, but adds it in period t + 1. Negative instances refer to events where the customer does not have
product i both in periods t and t + 1. On the other hand, when the customer has product i in
her portfolio in period t (regardless of whether or not she has it in period t + 1), we do not create
an observation. In our experiments, we work with the 20 products that have sufficient number of
3
The Current-Use and Ever-Used variables are calculated for all products, while the Returns variables are calculated
only for products that were present over the entire time horizon to avoid missing values. Hence we have 30 Returns
variables.
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positive instances4 both in the training and holdout datasets to facilitate evaluation of the accuracy. We train a logistic regression model for each product and variable set combination, in total
320 models, and evaluate them on the holdout data sets. Across products, the number of training
observations range from 84,900 to 222,000, and the number of test observations range from 9,148
to 24,660. Percent of positive instances varies from less than 0.01% to 4% across products; that is
to say, we are predicting rare events, which is relevant for our choice of the model.
Based on prior findings that training with balanced data in terms of positive and negative
instances can improve the prediction performance when dealing with rare events, (Weiss 2004,
Estabrooks et al. 2004, Laurikkala 2001), we explored different sampling schemes. We experimented
with combinations of over-sampling the rare class with the popular SMOTE method 5 (Chawla et al.
2002), and under-sampling the majority class randomly to reduce the imbalance in the datasets.
We used the wrapper methodology to identify the right combination of over- and under-sampling
(Chawla 2009). As these approaches did not improve the predictive accuracy of our models, we we
omit these results here.
Next, we report the accuracy of the logistic regression models on the holdout datasets. Classification accuracy of logistic regression models depends on the probability threshold value that is
used. We use the AUC (area under the receiver operating characteristics curve 6 ) measure, which
considers the performance for all possible threshold values. AUC provides the probability that a
classifier will rank a randomly chosen positive instance higher than a randomly chosen negative one
and it is commonly used to evaluate rare event classifications (Bradley 1997). The AUC value of 0.5
corresponds to random ranking, while 1 indicates perfect ranking of customer-month observations
in terms of product adoption probability. Table 1 provides the holdout (test) AUC measure for
each product and variable set combination. For example, for Product 1, the AUC for the logistic
4
Minimum 15 positive instances in the holdout and minimum 135 positive instances in the training datasets.
5
SMOTE creates synthetic observations as a linear combination of existing observations.
6
The receiver operating characteristics curve (ROC curve) graphs the true positive rate (percent of positives identified)
versus the false positive rate (percent of negatives identified as positive) for all threshold values.
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regression model that uses only the Current-Use information set is 0.69, while the model that uses
both the Current-Use and the Ever-Used sets has an AUC of 0.76; finally the model that uses all
132 variables has an AUC of 0.90. For each product, the highest AUC values among the models
using variables from a single information set are printed in bold, while the maximum AUC values
across all models are highlighted. We find that the All Vars models, that use all information sets,
provide the best test accuracy (based on holdout data) for 15 out of 20 products.
Table 1
Variable Sets
Current-Use
Ever-Used
Demographics
Economic Ind.
Returns
No. of Input vars
Product1
Product2
Product3
Product4
Product5
Product6
Product7
Product8
Product9
Product10
Product11
Product12
Product13
Product14
Product15
Product16
Product17
Product18
Product19
Product20
Average normalized AUC
Test AUC for all product and information set combinations
Models with Single Information Set
x
x
x
x
x
41
41
10
10
30
0.69
0.75
0.61 0.75
0.84
0.70
0.71
0.54 0.76
0.77
0.66
0.67
0.55 0.78
0.79
0.71
0.71
0.50 0.73
0.77
0.69 0.73
0.49 0.65
0.68
0.74
0.73
0.59 0.71
0.74
0.67
0.67
0.69 0.57
0.56
0.78 0.80
0.54 0.61
0.61
0.83 0.90
0.56
—
0.51
0.75 0.79
0.62 0.56
0.56
0.67 0.69
0.53 0.61
0.63
0.80 0.84
0.59 0.60
0.56
0.64 0.72
0.52 0.60
0.61
0.78 0.81
0.44 0.51
0.60
0.73 0.75
0.59 0.54
0.59
0.77 0.81
0.64 0.56
0.63
0.74 0.79
0.64 0.61
0.67
0.67 0.76
0.58 0.51
0.51
0.65 0.71
0.59 0.62
0.61
0.69 0.74
0.62 0.62
0.65
88% 92% 70% 73%
79%
x
x
40
0.84
0.77
0.79
0.77
0.69
0.76
0.58
0.62
0.51
0.57
0.63
0.59
0.64
0.54
0.61
0.63
0.67
0.52
0.62
0.65
79%
x
x
20
0.75
0.77
0.79
0.73
0.65
0.73
0.69
0.62
0.56
0.63
0.61
0.64
0.60
0.48
0.60
0.63
0.66
0.58
0.64
0.67
80%
Models with Two Information Sets
x
x
x
x
x
x
x
x
x
x
x
x
40
51
71
51
51
71
0.84 0.84
0.89
0.74 0.82 0.88
0.78 0.83
0.84
0.71 0.81 0.82
0.80 0.82
0.83
0.68 0.80 0.82
0.77 0.78
0.82
0.71 0.79 0.83
0.68 0.77
0.78
0.74 0.74 0.75
0.75 0.81
0.83
0.75 0.82 0.84
0.71 0.67
0.67
0.69 0.69 0.69
0.62 0.82
0.82
0.80 0.79 0.79
0.53 0.91
0.90
0.89 0.83 0.85
0.63 0.80
0.79
0.79 0.76 0.75
0.64 0.73
0.74
0.69 0.70 0.71
0.62 0.85
0.83
0.84 0.82 0.81
0.62 0.77
0.76
0.72 0.67 0.68
0.52 0.81
0.82
0.80 0.78 0.79
0.62 0.77
0.78
0.75 0.73 0.73
0.67 0.83
0.85
0.83 0.78 0.79
0.71 0.82
0.83
0.80 0.77 0.79
0.58 0.78
0.78
0.76 0.67 0.67
0.64 0.75
0.75
0.73 0.68 0.68
0.70 0.76
0.80
0.75 0.74 0.77
82% 97% 98% 93% 93% 94%
x
x
x
x
51
0.68
0.70
0.66
0.70
0.69
0.74
0.71
0.78
0.87
0.75
0.67
0.79
0.64
0.76
0.73
0.79
0.77
0.66
0.67
0.71
89%
82
0.76
0.75
0.69
0.74
0.74
0.77
0.70
0.82
0.87
0.80
0.71
0.84
0.73
0.80
0.76
0.84
0.81
0.77
0.72
0.74
94%
All Vars.
x
x
x
x
x
132
0.90
0.84
0.84
0.83
0.77
0.85
0.71
0.83
0.89
0.81
0.74
0.84
0.79
0.82
0.78
0.87
0.85
0.79
0.76
0.79
100%
The bottom row of the table displays the normalized AUC for the variable set averaged across
products, where normalized values express AUC as a fraction of the model with All Vars. We
observe that the Ever-Used information set with 41 variables provides on average 92% of the AUC
that is achieved by using all 132 variables. This is consistent with the prior finding that product
usage reflects the customer’s financial maturity, and is important in product choice (Li et al.
2005). It is also consistent with the recommender systems literature that uses customer’s previous
purchases to provide a new product recommendation using the patterns of other customers with
similar product purchasing patterns (Adomavicius and Tuzhilin 2005). Ever-Used information set
characterizes the customer experience and preference via past product use.
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The second best single information set is Current-Use with average normalized accuracy of 88%.
This is consistent with Knott et al. (2002), who found that current ownership is predictive of subsequent product choice. Conceptually, using this information set allows the model to offer products
“that go with” the products the customer currently holds in the portfolio. On the other hand,
it may not fully reflect the customer’s level of financial maturity and investment preferences, as
the customer may be holding only those financial products in the portfolio that seem appropriate for the specific environmental – both macroeconomic and customer-specific microeconomic –
conditions.
Even though the average predictive accuracy of Returns is only 79% of the full model, for 5
of the 20 investigated products, it provides the best accuracy among the single information set
models, and in 3 of these model, Returns AUC is significantly higher than the Ever-Used AUC
at the .05 level (see DeLong et al. (1988) for details of the statistical test of AUC differences). In
13 products, the Ever-Used information set results in statistically significantly higher AUC values
than Returns. Examining the characteristics of products that are predicted better with the Returns
information set than the Ever-Used set, we find that they are less liquid and involve higher risk
(as measured by the return variability).
Economic Indicators provide on average only 74% of the AUC of the All Vars models, and their
accuracy is not significantly better than the Returns models for any product. Demographics on
their own provide a fairly low average normalized accuracy of 69%.
Table 2 shows the correlation of the predicted probabilities produced by models of single information sets. The Returns and Economic Indicators models are highly correlated, while the models
using Ever-Used and Returns produce the least similar predictions. Ever-Used variables reflect
customer’s past experience with financial products but do not take the environmental conditions
into account. In fact, models with this set of variables assign the same product adoption probability, in consecutive periods, unless she has tried a new product in the meantime. On the other
hand, the Returns models assign the same probability to all customers in the same time period.
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In cross-sell terminology, the first model focuses on the right customer regarding the customer’s
internal progress, whereas the second focuses on the right time for suggesting the product. Therefore, it is not surprising that the Ever-Used and Returns information sets together provide 98% of
the full model AUC. In fact, this smaller model performs better than the full model in 3 of the 20
products. Adding more variables will always provide better accuracy in the training data, but as in
this case, overfitting may result in inferior holdout accuracy. None of the differences between the
test AUCs of Ever-Used and Returns models versus All Vars model were significant at .05 level.
In conclusion, we use Ever-Used and Returns information sets together in our product-specific
predictive models for adoption probabilities.
Table 2
Correlation coefficients for predictions produced by models using single variable sets
Pearson Correlations Current-Use Ever-Used Demographics Returns Economic Ind.
Current-Use
Ever-Used
Demographics
Returns
Economic Ind.
1
0.66
0.63
0.55
0.57
1
0.64
0.54
0.56
1
0.85
0.88
1
0.96
1
Finally, note that although we estimate binary logistic regression models for each product independent of the others, since we use the same information sets, any potential dependency between
product acceptance probabilities is captured via the customer’s product use history ( Ever-Used )
and the current product returns (Returns). Another issue is the possible existence of multicollinearity within information sets. However, Shmueli and Koppius (2011) argue that predictive analytics
and explanatory statistical modeling are fundamentally disparate – among the key differences is
the treatment of multicollinearity. For purposes of prediction, which is our primary goal for using
the binary logistic regression models, multicollinearity is not as problematic as it is for explanatory
modeling (Vaughan and Berry 2005). While perfectly correlated variables do not increase predictive accuracy, very highly correlated variables can add predictive power over and above using one
of the two variables (Guyon and Elisseeff 2003). Indeed, our additional experiments where we omit
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the information sets with high multicollinearity and instead use their uncorrelated principal components (see Rao 1964) do not improve predictive accuracy of our models. We omit these results
for brevity.
3.2.2.
Mapping Adoption Probabilities to Acceptance Probabilities. We use the Ever-
Used and Returns variables and the available dataset from ykpb (without train-test distinction and
no over- or under-sampling) to estimate a logistic regression model for each product i, and use the
predicted adoption probabilities p̂it as inputs to our win-win cross-selling model for each customer.
We map the adoption probabilities to acceptance probabilities using (35). In our application,
we choose Φ such that the median adoption probability of 0.02% (pooled across all customers
and products) takes the value of the ξ-th percentile of the adoption probability distribution. For
example, ξ = 50% implies Φ = 1, whereas ξ = 90% corresponds to Φ = 34, bringing the median
acceptance probability to 0.68%. We refer to ξ as the effectiveness of the cross-selling effort of
the bank. Note that the higher the ξ, the more likely that the offer is accepted by the customer.
For October 2010, the average product adoption rates vary between 0.0004% and 2.57%, with
an average of 0.39%, per customer per month, clearly indicating that the bank’s customers do
not readily adopt products which are not in their current portfolios. This observation highlights
the need for cross-selling in this particular setting. With a ξ = 90% cross-selling effectiveness, we
map these aforementioned adoption rates to acceptance probabilities with a range of 0.014% and
44.95%, and an average of 9.57%.
Figure 5 presents the average acceptance probabilities (for non-users) of the 41 products in
various asset classes of the bank as a function of their expected returns in October 2010. Notice
that the products that customers tend to find more acceptable have relatively lower returns. The
reason for this may be that products with higher returns are mostly associated with higher risks
(as previously shown in Figure 2), or such products may be more sophisticated products that
customers are not accustomed to.
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Acceptance Probability
28
C om m od ity
E q u ities
F ix ed incom e
M oney m ark et
Alternativ e prod u cts
E x pected R etu rn
Figure 5
3.3.
Product acceptance probability as a function of product return for ξ = 90%
Cross-Selling with Win-Win
In this section, we first compare the performance of our win-win portfolio selection policy ( ww)
with three benchmark policies – the mean-variance policy without cross-selling (mv), which only
considers a rational customer’s portfolio objectives, the mean-variance policy with cross-selling
(mvc), which considers a rational customer’s portfolio objectives as well as the acceptance probabilities, and the greedy policy (gr), which considers the bank’s short term profitability and
acceptance probabilities (Figure 6 illustrates which key model features are taken into account by
each benchmark policy and the win-win approach). Then, we explore the sensitivity of the performance measures of the proposed policy to key operational levers. In the following, we explain the
benchmark policies in more detail.
Figure 6
Overview of features captured by benchmark policies
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Mean-Variance Policies: The two mean-variance policies, mv and mvc, are built on the Modern
Portfolio Theory (MPT), as explained in Section 2, with the following distinguishing features. First,
they both allow only one product to be added to the current customer portfolio, and the weight
ˉ Second, variance of the proposed portfolio return cannot
of the new product is bounded by Ω.
exceed that of the current portfolio. In other words, the variance bound σ 2 in (4) is operationalized
as the current portfolio risk. Third, the proposed portfolio return cannot be lower than that of
the existing portfolio. These additional features allow us to make a fair comparison between the
mean-variance policies and ww.
mv, mean-variance policy without cross-selling, has two key differences with ww. First, the
objective function is to maximize Rt+1 (wt+1 ) rather than to maximize R̃t+1 (wt+1 ), i.e., mv ignores
the acceptance probabilities. Therefore, the policy pretends that a customer will accept the offer
that is developed on her behalf to optimize her portfolio. Moreover, mv overlooks the impact of
the proposed portfolio on bank profitability, which is captured by (24) in ww. On the other hand,
mvc, mean-variance policy with cross-selling, takes acceptance probabilities into account when
computing the expected return of the proposed portfolio, just as ww does in (19), yet fails to
consider bank profitability similar to mv.
Greedy Policy. This policy simply offers the product with the highest expected bank profit
that is currently not being used by the customer, and the weight of the offered product is
ˉ again. We refer to this cross-selling model, which completely overlooks the
assigned to be Ω,
impact of the offer on customer portfolio returns and risk, as gr. This policy identifies prodˉ and wj,t+1 = (1 −
uct j ∗ = arg max {θjt πj | ∀j : wjt = 0} and assigns portfolio weights wj ∗ ,t+1 = Ω
ˉ jt , ∀j ∈ Pt .
Ω)w
In our experiments, we assume that ykpb makes product offers to its customers in October
2010. When making offers, ww and gr use the acceptance probabilities computed by the predictive
model for October 2010, and ww and mv rely on the estimated product returns for November
2010. Clearly, the success of our model (as in any portfolio selection model) depends on the quality
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of estimates of the future returns. We use simple averages for this purpose in our experimental
results, which performs reasonably accurate for November 2010 (improving the estimation accuracy
is beyond the scope of this paper).
We assume customers make their decisions (whether to accept or reject the bank’s offers) based
on their respective acceptance probabilities. Then, we evaluate customer portfolios under these
four policies (mv, mvc, gr, and ww) using actual November 2010 returns in terms of the following
performance measures:
ΔR̃
: average expected percentage change in portfolio returns over all customers
ΔΠ̃
: expected percentage change in bank profitability averaged over all customers
ΔΠ̃t : expected percentage change in total bank profits
In order to distinguish between the performance of various policies, we use the policy name as an
index (subscript) with the particular performance measure when necessary.
We
focus
on
three
key
operational
levers:
Bank’s
cross-selling
effectiveness
(ξ ∈
{50%, 70%, 90%, 95%, 99%}), minimal requirement for desired bank profitability increase per cus-
ˉ∈
tomer (Δπ ∈ {0%, 5%, 10%, 20%}), and maximum allowable weight of the offered product ( Ω
ˉ for all customers, i.e., the absolute
{10%, 20%, 40%}). Here, we assume the same value for Ω
investment amount of the proposed product can essentially be larger for a customer with a larger
portfolio size. This implies that customers are concerned with the relative amount of the investment
rather than its absolute value. Note that our methodology can easily be adapted to accommodate
ˉ with portfolio size (see Section 3.4).
increasing or decreasing Ω
As our base scenario, we consider a bank with a cross-selling effectiveness of 90% (ξ = 90%), a
minimum 10% profit increase requirement (Δπ = 10%), and a maximum allowable change of 20%
ˉ = 20%). We generate other test scenarios by systematically varying these
in portfolio weights (Ω
parameters from this base scenario. We first present a comparison of the four policies for the base
scenario in Table 3.
Both mv and mvc policies provide offers to 6,633 customers (94% of customers), while 388
customers do not receive one, because their portfolios could not be improved by adding a single
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Table 3
31
Summary comparison of mv, mvc, gr and ww for the base scenario
Policy
ΔR̃
ΔΠ̃
ΔΠ̃t
mv
mvc
gr
ww
0.81%
26.19%
−15.32%
6.06%
−0.03%
−0.02%
−0.85%
29.76%
11.29%
1.10%
39.28%
13.74%
product by these two policies. We observe that the change in portfolio returns Δ R̃mv is very small
(ΔR̃mv = 0.81%) under mv. We note that if all offers were accepted, the increase in returns would
have been much higher, 229.47%. However, it seems that offers that will increase portfolio returns in
a Markowitz fashion turn out to be the ones that the customers are not likely to accept (as can also
be seen in Figure 5). We conclude that, not considering acceptance probabilities when making offers
does not result in any significant realized benefit for customers on average. We support this claim
by comparing ΔR̃mv with the realized benefits under mvc (ΔR̃mvc = 26.19%). Clearly, taking the
acceptance probabilities into account drastically improves the performance of the mean-variance
policy. Moreover, mv and mvc do not result in appreciable changes in the bank profitability either:
The expected change in per customer profitability (Δ Π̃mv = −0.03% and ΔΠ̃mvc = −0.85%), and
the change in total bank profitability (Δ Π̃tmv = −0.02% and ΔΠ̃tmvc = 1.1%) are negligible. This is
not surprising, since these policies do not take bank profitability into account while making offers.
The gr policy, on the other hand, makes offers to all customers and leads to the highest increase
in bank profits (ΔΠ̃gr = 29.76% and ΔΠ̃tgr = 39.28%), as implied by its main objective. However,
it achieves this result at the expense of customers’ portfolio returns, which decrease by 15.32% on
average. Even if customers may go along with the suggestions of this greedy cross-selling policy
(as it considers their acceptance probabilities), investment portfolios that fail to appreciate in time
will increase customer propensity to churn, with a potential to reduce bank profitability to a much
larger extent than what was originally achieved by cross-selling. Obviously, gr, which appears to
serve the bank’s profitability objective in the short term, is not a sustainable policy if the bank
wants to retain its customers in the long run.
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The proposed ww policy strives to serve both customers’ and the bank’s interests while considering acceptance probabilities. In choosing the product to offer, ww applies more discretion (via
an additional bank profitability constraint) compared to mv and mvc, therefore a smaller set of
customers (6034 customers) are offered new products. However, ww still manages to achieve a
substantial improvement in both the customer returns and bank profitability. Across all customers,
the average improvement in expected portfolio returns is 6.06%, the average improvement in per
customer bank profitability is 11.29%, and the increase in total bank profits is 13.74%. Thus,
ww results in a win-win situation in the customer-bank relationship. We observe that ww results
in a significant benefit for the customers (Δ R̃ww = 6.06% > 0.81% > −15.32%). Although, the
expected profit improvement under ww is not as high as that under gr, it is still considerably
high. As a result, ww represents a fair balance between the customers’ and the bank’s objectives.
Table 4
Table 5
Impact of bank’s cross-selling effectiveness (ξ) on ww performance
ξ
ΔR̃ww
ΔΠ̃ww
ΔΠ̃tww
50%
70%
90%
95%
99%
0.19%
1.31%
6.06%
12.84%
46.61%
0.35%
2.46%
11.29%
23.03%
52.97%
0.43%
3.02%
13.74%
28.23%
61.71%
Impact of minimal requirement for desired bank profitability increase per customer (Δ π) on
ww performance
Δπ
ΔR̃ww
ΔΠ̃ww
ΔΠ̃tww
0%
5%
10%
20%
7.53%
6.60%
6.06%
5.45%
11.39%
11.50%
11.29%
10.76%
14.11%
14.20%
13.74%
13.07%
Next, we study the impact of key operational levers, i.e., effectiveness of the bank’s cross-selling
efforts (ξ), bank’s minimum profit increase requirement (Δπ), and the maximum allowable change
ˉ on the three performance measures under ww.
in customers’ portfolio weights ( Ω),
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Table 6
33
ˉ on ww performance
Impact of maximum allowable weight of the offered product ( Ω)
ˉ
Ω
ΔR̃ww
ΔΠ̃ww
ΔΠ̃tww
10%
20%
40%
2.43%
6.06%
12.71%
5.1%
11.29%
24.02%
6.43%
13.74%
29.52%
As the effectiveness of the selling effort ξ increases, the improvements in the customer returns,
ΔR̃ww , and bank profit, in terms of average percent profitability and total bank profits, Δ Π̃ww
and ΔΠ̃tww , increase as seen in Table 4. When the bank demands a higher minimum increase in its
profitability per offer Δπ, the portfolio selection problem of each customer becomes more restrictive.
As we previously stated in Lemma 2(iii ), the number of customers without any offers increases
with Δπ. Further, the bank profitability from the customers with offers increases, as we also claim
Lemma 2(ii ). Consequently, the overall impact of an increase in Δπ does not necessarily translate
into improved profitability for the bank. As per the customer returns, a larger Δπ leads to a smaller
feasible set of products that can be offered. Thus, there is clearly less room for improvement in
customer returns, as seen in Table 5 (and as stated in Lemma 2(i )). Table 6 shows that all key
performance measures improve as ww is allowed to make more changes in the customers’ portfolios
ˉ increases). This insight is already stated in Lemma 1. However, our empirical results indicate
(as Ω
that the improvement in customer returns and bank profitability can indeed be substantial.
3.4.
Robustness of the Win-Win Approach
In this section, we go beyond the sensitivity analyses for the operational parameters, reported in
Section 3.3, and provide additional experimental results regarding the robustness of our win-win
approach with respect to three key modelling choices.
Financial Framework. Instead of the mean-variance approach from the Modern Portfolio Theory
(MPT) for portfolio selection, one could also adopt the Capital Asset Pricing Model (CAPM)
framework. In CAPM, the systematic risk associated with individual products is represented by
the so-called beta (β). Nevertheless, the risk of a “properly” selected (diversified) portfolio only
depends on the systematic risk associated with the market. To implement CAPM, we (i) computed
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the β and expected return for each product from our dataset, (ii) obtained the risk-free return
rate based on Turkish government bonds, (iii) calculated the market return rate as a weighted
average of returns from four classes of assets, namely fixed deposits, foreign exchange, Istanbul
stock exchange index, and bonds, and (iv) adapted the return and risk formulations given in (7)
and (8) to the CAPM. In the following table, we compare the results under the MPT and CAPM
frameworks considering the base scenario; we observe that the qualitative nature of the results
from MPT and the CAPM approaches are the same. Hence, our optimization approach is robust
with respect to the choice of the financial framework.
Table 7
Comparison of results under MPT and CAPM frameworks
MPT
CAPM
Policy
ΔR̃
ΔΠ̃
ΔR̃
ΔΠ̃
mv
mvc
gr
ww
0.81%
26.19%
−15.32%
6.06%
−0.03%
0.06%
12.99%
−15.32%
5.29%
−0.03%
−0.85%
29.76%
11.29%
−5.56%
29.76%
6.96%
ˉ represents the limit on the weight of the new
Weight of the New Product. The parameter Ω
ˉ for all customers.
product in the customer’s portfolio. So far, we have assumed the same value for Ω
This implies that the limit on the absolute amount to be invested in the proposed product is larger
ˉ could possibly depend on the total wealth level of a customer.
for a wealthier customer. However, Ω
ˉ is to categorize the customers into tertiles based
One way of implementing a wealth dependent Ω
ˉ M and Ω
ˉ H denote the limits for customers with Low, Medium,
ˉ L, Ω
on their “level of asset”. Let Ω
and High asset levels, respectively. In Table 8, we present the the performance of the ww policy
ˉ M and Ω
ˉ H . Specifically, we consider the cases in which the
ˉ L, Ω
for different combinations of Ω
limit increases (first two rows) as well as decreases (last two rows) with wealth. We observe that
our approach still yields significant benefits to both the bank and the customers in all considered
settings.
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Table 8
35
ˉ 1, Ω
ˉ 2 and Ω
ˉ 3 on the ww performance
Impact of Ω
ˉL
Ω
ˉM
Ω
ˉH
Ω
ΔR̃ww ΔΠ̃ww
10%
15%
20%
25%
30%
20%
20%
20%
20%
20%
30%
25%
20%
15%
10%
5.38% 10.00% 15.13%
5.21% 9.82% 13.15%
6.06% 11.29% 13.74%
4.71% 9.48% 9.10%
4.47% 9.32% 7.07%
ΔΠ̃tww
Adoption-to-Acceptance Mapping Function. We capture the bank’s cross-sell effort through
a piece-wise linear function, discussed in Section 3.2, which maps a customer’s adoption probability
to her acceptance probability. As an alternative, we now consider the concave mapping θit = f (p̂it ) =
(p̂it )α where α ∈ [0, 1]. When α = 1, cross-selling has no effect on acceptance (θit = p̂it ), whereas
when α = 0, cross-selling has the maximum impact (θit = 1). Table 9 reports the performance of
our win-win methodology using this mapping function.
Table 9
Impact of the bank’s cross-sell effectiveness (α) on ww performance using θit = (p̂it )α
α
ΔR̃ww
ΔΠ̃ww
ΔΠ̃tww
0.0
0.2
0.4
0.6
0.8
1.0
208.01%
43.82%
6.12%
1.34%
0.44%
0.19%
59.24%
13.85%
4.54%
1.8%
0.76%
0.35%
50.86%
15.98%
5.31%
2.11%
0.91%
0.43%
Note that the case α = 0 (all offers are accepted by customers) gives an upper bound on the
potential benefits of ww. As α increases, the effectiveness of the offers diminish, and hence Δ R̃ww ,
ΔΠ̃ww and ΔΠ̃tww decrease. The case α = 1 (cross-selling has no effect) corresponds to ξ = 50%
in Table 4. Overall, we observe that our methodology produces benefits for the customer and the
bank, regardless of the particular form of the mapping function.
4.
Real Life Implementation at Yapı Kredi
Yapı Kredi implemented a decision support system, named “Golden Offer”, and launched a pilot
application to assess the real life impact of the proposed approach in the first half of 2013. Based on
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the realized success in the pilot application, ykpb made the system available to all of its customers
in 2014.
Note that ykpb’s customer base changes over time. Our win-win model, as described in Section
2.2, is solved for each individual customer separately at any given period. Once sufficient behavior
data for a new customer is accumulated, an rm would be able to offer new products using Golden
Offer. ykpb also updates the product-specific predictive models for adoption probabilities periodically (every 6 months) to capture any potential changes in the behavioral patterns of customers
with respect to product returns.
In this section, we briefly overview the system architecture for the implementation at ykpb, and
then present the challenges and relevant benefits of this application.
4.1.
System Architecture
Yapı Kredi Bank has a mature datawarehouse (DWH) system which has been operational since
2001. DWH has more than 20,000 tables with over 600,000 columns in total, and uses Sybase-IQ
as its relational database management system (RDBMS) platform. DWH data is daily refreshed
from the Operational Data Store (ODS) which is replicated near-online from core banking systems.
Figure 7 provides an overview of the system architecture for the implementation of our solution as
Golden Offer within the bank infrastructure.
Figure 7
Overview of the system architecture at ykpb
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The Private Banking Datamart, containing 171 tables with a total of 2,861 columns, stores the
key ingredients required for Golden Offer; namely investment transactions, product holdings, asset
transfers and customer level aggregations, as well as product price data gathered from market data
providers to DWH system. Golden Offer is implemented in the CRM intranet application (developed in-house with Microsoft .NET C# and uses Microsoft SQL Server as its database server). The
predictive models for offer acceptance probabilities are developed with the SAS software (Prediction Engine in Figure 7), and the win-win cross-selling models are solved using the Solver add-in of
Microsoft Excel (Optimization Engine in Figure 7). Whenever an rm utilizes the system to generate a Golden Offer for an investment product suggestion to a private banking customer, the add-in
runs at the application server and sends the results back to the CRM Application Frontend. The
rm then communicates the Golden Offer to the customer via before–after portfolio composition,
risk-return visuals. A sample visual is provided in Figure 8.
ykpb uses SAP Business Objects as its main business intelligence reporting platform. This tool
is connected to the Private Banking Datamart and reports about portfolio returns, investment
transactions and Golden Offer system usage can be queried by headquarters.
4.2.
Challenges in Implementation
While launching the system, ykpb had its fair share of challenges. First, many rms initially shared
the view that they knew the customer best due to their interactions at a personal level. They
believed that private banking, unlike retail banking, could not be managed by analytical/system
support approaches. Hence, rms had to be convinced that the new system was in their interest
as well. Accordingly, ykpb upper management ensured that the rms’ incentives were aligned with
the objectives of Golden Offer (e.g. avoiding product-specific sales quotas). Then, before launching
the system, they organized a training and information convention for the rms to communicate the
benefits of Golden Offer for the customers, the bank, and the rms themselves. A second potential
concern was that, receiving computer assisted investment offers itself was a new phenomenon for
most customers; and the ykpb management was not certain about the customer appreciation of
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Figure 8
Screenshot from ykpb’s Golden Offer
the process. It turns out that customer feedback was generally positive in this respect. Finally,
Golden Offer would be run by rms at the branch office, but not all customers visit the offices.
Although the rm could still suggest the investment offer to such a customer by phone or email,
showing potential results on the computer would be much more effective.
4.3.
Real Life Benefits
The real life impact of Golden Offer was assessed by ykpb after a 6 month long pilot study that took
place in the first half of 2013. A convenience sample of 501 private banking customers participated
in the pilot study. These customers received at least one Golden Offer during the pilot period.
In order to measure the impact of Golden Offer, we compare the change in the performance
measures of the pilot customers with their control group. Directly comparing the pre and post
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performances of the pilot group may be misleading; the difference may be simply due to environmental factors, such as the economy. Further, we need to consider (i) potential selection bias of
pilot customers and (ii) potential mismatch in the pre-pilot period performance of the pilot and
control customers. To alleviate the selection bias, we use the propensity score matching technique
(Caliendo and Kopeinig 2008). We estimate the selection probability with a logistic regression
model that predicts whether or not the customer participates in the pilot using customer demographics (e.g. age, gender) and portfolio characteristics, (e.g., portfolio size, number of products,
portfolio profitability and return in the period before the pilot). We match each pilot customer
with her ten nearest non-pilot neighbors in terms of selection probability using their propensity
scores. We note that the propensity score matching process was successful as the average difference
in propensity scores of the pilot and their control customers was very low (0.0007). Further, to
eliminate a bias due to potential mismatch of pre-pilot period performance, we use the difference in
differences approach (Card and Krueger 2000), where we compare the performance improvement
(or decay) in the pilot versus their control customers. The comparison period was six months before
versus during the pilot period. The difference in differences approach is based on the premise that,
in the absence of the treatment, the environmental factors will affect the performance of the treatment and control groups similarly. As a result, we observe that both groups of customers increased
their portfolio returns during the pilot study. However, the average portfolio returns of customers
in the pilot group increased 17% more than that of the customers in the control group. Further,
ykpb profits per customer in the pilot group increased an additional 7.9% compared to the control
customers.
In addition to the immediate and primary benefits presented above, there are other benefits
of the particular implementation at ykpb. First, adopting new products is expected to help the
customer move along the financial maturity spectrum and render more products acceptable in the
long run (Kamakura et al. 1991). On a related issue, buying new products may actually increase
switching costs (Kamakura et al. 1991). This is because a customer now must move more products
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to a competitor. On this aspect, during the pilot application, the average number of products in
the customer portfolios increased by 0.41 versus 0.19 for the pilot group and the control customers,
respectively. Secondly, using an analytical tool such as Golden Offer increases the consistency
of investment suggestions made by the rms. As these results point to substantial gains for the
customers and the bank, ykpb decided to make Golden Offer available to all private banking
customers starting 2014. ykpb achieved increases in customer satisfaction scores in both 2014
and 2015 (as regularly measured by an independent research company). The bank management
attributes part of this success to Golden Offer. Further, ykpb won the Innovation in Private
Banking award from the Private Asset Management magazine (published in the United States) in
2014 (URL: www.pammagazine.com/pam-awards-2014) for Golden Offer.
5.
Concluding Remarks
In this paper, we propose a novel approach to investment product cross-selling that enables a
sustainable relationship between customers and their bank by considering their interests simultaneously. Our approach also considers the customers’ likelihood of accepting the offered products, thus
avoiding offers that are not acted upon by customers. The proposed win-win approach combines
the following key aspects: First, the offer (if made) improves both the customer’s portfolio and the
bank’s profitability. Second, customer’s likelihood of accepting the offer is predicted from readily
available data. Third, customer’s existing portfolio is taken as the starting point.
We illustrate our methodology by using data from Yapı Kredi Private Banking. We first find
that the list of previously used products by the customer and and recent product returns can be
used for predicting the customer’s propensity to accept an offer from the bank. Second, the real
life implementation of our solution approach (during a six month pilot study in the first half of
2013) increased bank profitability and customer portfolio returns, essentially creating a win-win in
the bank-customer relationship.
Finally, we would like to remark on a number of potential limitations of our approach. First, we
assume that the customer’s acceptance probability is independent of the “weight” of the offered
Author: Cross-Selling Investment Products
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41
product. One might expect that the this probability would decrease if the new product offer calls for
a larger investment amount. Our current model does not address this issue. Second, our framework
implicitly assumes that all relevant financial assets of the customer are held by the bank. In other
words, the portfolio as known to the bank should be a good proxy of the customer’s true portfolio.
In the particular application reported in this paper, we have reason to believe that this is indeed
the case – a previously conducted survey by the bank to a sample of customers indicated that
majority of the participants either had all or at least 2/3 of their assets with the bank. If a customer
has a sizeable outside investment and is willing to share the relevant information with the bank,
our approach can still be used. Third, we assume a particular fee structure to account for bank
profitability consistent with the application setting, yet our model can be extended to alternative
fee structures, such as one-time transaction fees.
Acknowledgments
This research was supported by the Scientific Council of Turkey, Project number TEYDEB 1501-3100085. The
authors thank İmre Tüylü and her team from Yapı Kredi Bank for her outstanding support of the research
project. The authors also thank the associate editor and referees for helpful comments and constructive
suggestions that significantly improved this paper.
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Özden Gür Ali is an associate professor in the Operations Management and Information Systems Area of the College of Administrative Sciences and Economics, Koç University. Her current
research is in predictive analytcs, data mining in retail, banking and healthcare; particularly in
sales forecasting in the presence of promotions, customer behavior models.
Yalçın Akçay in an associate professor in the Operations Management Area of the College of
Administrative Sciences and Economics, Koç University. His research focuses on revenue management, dynamic pricing, inventory management, retail operations, stochastic modeling of service
and manufacturing systems.
Serdar Sayman is an associate professor in the Marketing Area of the College of Administrative
Sciences and Economics, Koç University. His research interests include behavioral decision making
and modeling retail strategies.
Mehmet Hamdi Özçelik is the Marketing Analytics and Optimization Manager at Yapı Kredi
Bank. He also gives lectures on Big Data Analytics at various Turkish universities.
Emrah Yılmaz was a Ph.D. student in Business Administration at Koç University. He now works
as a manager at the Advanced Analytics Department of Emirates Integrated Telecommunications
Company, Dubai.