State Street’s Digest of
Topics in Securities Finance
In View
ISSUE 1 |
The Value and Cost of Borrower Default Indemnification
NOVEMBER 2013
In View Series
As one of the world’s most experienced
Pending and proposed regulatory changes with regards to capital charges have
lending agents providing both custodial
prompted discussions within the securities lending industry about agent banks’
and third-party lending, State Street
capital usage and business models, particularly with respect to borrower default
offers the individualized service, client-
indemnification. This article, our first on the subject, presents a general framework
facing technology and commitment to
describing how agents and lenders may value the potential cost and benefit of a
transparency you’re looking for.
borrower default indemnity. A future article will delve into greater detail, modeling
Whatever the market conditions, our
specific transactions common to securities lending. It is our hope that these pieces
dedicated team can work with you to
may provide industry participants with a firmer foundation for open dialogue about
design a program within a framework
optimal lending program structures, which may vary based upon beneficial owners’
tailored to your return objectives and
individual assets and risk appetites.
risk appetite. The In View Series
highlights topical issues for today’s
Historically, agent lenders have provided many beneficial owners with an
securities finance market.
indemnification against borrower default in their securities lending programs. These
indemnities generally have not been explicitly priced into the cost of agency
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securities lending and often agents have viewed the indemnity provision as a cost
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of winning business. This view may change in coming years given that the cost to
specialized research, trading, securities
agent lending banks of supplying these indemnities may increase significantly due
lending and innovative portfolio
to changes in the regulatory environment under the Dodd-Frank Act (DFA) in the
strategies to owners and managers of
U.S. and Basel III globally. We think it prudent, then, that industry participants try to
institutional assets.
gain a better understanding of the dollar value of such indemnities for beneficial
owners as well as the potential future cost to agent lenders to provide them.
Author
Valuing an Indemnity: A Conditional Option Pricing Model
Glenn Horner, CFA, FRM
+617 6645851
The value of an indemnity can be approximated using a conditional option pricing
[email protected]
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model . Conceptually, the beneficial owner writes a call option for which the current
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We use the Margrabe-Fischer conditional option pricing model, which collapses to the
Black-Scholes-Merton option pricing formula when the collateral portfolio consists solely of cash.
Current Value of Credit Exposure = [Ѕ1N(d) – Ѕ2N(d– σp√T)] Pr (borrower default)
where

d=[ln(S1/S2)+.5p2T] / [pT]
p = (12+22+212)½
and where S1 is the current market value of loan portfolio, S2 is the current market value of the collateral portfolio, 1 is the return volatility of the
loaned portfolio, 2 is the return volatility of the collateral portfolio,  is the correlation of changes in the loaned portfolio returns and changes in
the collateral portfolio, p is the standard deviation of a two-asset portfolio where asset 1 is the loaned security and asset 2 is the collateral
STATE STREET’S DIGEST OF TOPICS IN SECURITIES FINANCE |
IN VIEW
price of the underlying “security” is equal to the market value of the securities loaned, the collateral value is the strike price and
the buy in period is the time to expiry. The volatilities used are that of the underlying loan and collateral portfolios.
In using such a model we assume that the borrower, as the purchaser of the call option, has the option to not return the securities
that it has borrowed (and simultaneously forfeit the collateral pledged) if the call is in the money. However, within this theoretical
construct we accept that the borrower would not exercise unless forced due to insolvency, given both its contractual obligations
and expected severe reputational harm.
As an example, let’s assume that a beneficial owner has loaned $100 million in S&P 500 stock to a borrower and received 102%
cash collateral. Currently the beneficial owner has excess collateral and its agent would be able to buy back all of the securities
on loan in the case of borrower default. However, there is a chance that the value of the securities on loan increases and the
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collateral is then insufficient to repurchase all of the securities. Using the Black-Scholes formula , we can estimate the expected
value of potential states of collateral shortfall.
For example, let’s assume that the annualized volatility of the S&P 500 is 15%, that the buy-in period is 5 days and that the
annual risk-free rate is 15 bps. Given these parameters the theoretical value of a call option for the borrower is $115,357, or
approximately 11.5 bps. Since the borrower is assumed to not exercise the option unless it is forced to default, we can further
condition the value by the borrower’s probability of default. If we assume that the borrower’s annual probability of default is 2%
and assume that the loan profile will remain constant throughout the year, the value of all options to the borrower over the next
year, and the value of an indemnity to the beneficial owner, will be approximately $2,307 ($115,257*2%), or 0.2 basis points.
The above chart shows the potential loss in default at different loan portfolio values. There is no loss until the market value of the
securities loaned exceeds the value of the collateral. Thereafter, the loss in the event of default would match the change in loan
value. The below chart depicts the area under the return distribution for the loan portfolio for which a potential loss could occur.
security, and N(.) is the standard cumulative univariate normal distribution function. The above rests on the assumption that changes in the value
of securities out on loan and changes in the non-cash collateral value are uncorrelated with changes in the borrower's creditworthiness.
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Ibid.
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STATE STREET’S DIGEST OF TOPICS IN SECURITIES FINANCE |
IN VIEW
The Cost of Indemnification
Under the proposed and pending new rules, an agent lender’s calculated cost to provide borrower default indemnification may
exceed the expected monetary payout to a beneficial owner for an event of a default. More specifically, the cost to provide the
indemnity is generally expected to be higher due to an agent lender bank’s need to hold capital against indemnified loans, which
are factored into risk-weighted asset (RWA) calculations. Under Basel I, with exemptions provided by the Federal Reserve and
the Office of the Comptroller of the Currency, many banks utilize a Value at Risk calculation to determine the RWA associated
with securities lending. The risk weighting for banks and broker/dealers under Basel I is 20%, so the agent lender bank then
multiplies its calculated VaR by 20% to arrive at RWA. Using the same example as above and assuming a 5-day volatility of the
S&P of 2.5%, the approximate RWA for the indemnified loan activity under the current VaR methodology would be calculated as
follows:
th
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99 percentile VaR = (100,000,000 * (1+(0.025)*2.33) – 102,000,000 = 3,825,000
RWA = (3,825,000 * 0.2) = 765,000
If the bank were to have a target Capital/RWA ratio of 10%, the capital it would hold against the described indemnified loans
would be $76,500. Assuming a 12% cost of capital, the bank’s cost of holding that capital would be $9,180 or 0.9 basis points per
year.
Under Basel I, and in the example shown herein, the cost of capital associated with indemnifying securities lending is about 4x
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higher than the expected value of the collateral shortfall as estimated by valuing the call option (i.e., the expected value of the
indemnity to a beneficial owner). As we’ve described, the expected value of losses to an agent lender are generally quite low
because of the low expected probability of a borrower defaulting and because loans are over-collateralized. However, making
certain standard assumptions, the associated cost of capital is still a fraction of the revenue earned by agent lenders. As such,
agent lenders generally feel comfortable absorbing the cost of providing the indemnity in order to provide clients comfort that they
will not incur what could be a large loss in the rare event that a borrower defaults and the market moves in the wrong direction
(i.e., the value of the loans rise or the value of the collateral declines).
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For a standard normal distribution, the z-score for a one-tailed test with a 99% confidence value is 2.33.
Where expected value is the probability-weighted average of possible outcomes.
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STATE STREET’S DIGEST OF TOPICS IN SECURITIES FINANCE |
IN VIEW
As U.S. banks adopt Basel III, the Collins Amendment within DFA will require large banks to calculate regulatory capital ratios
using both an advanced and standardized approach and to apply the more conservative of the two. Under a standardized
approach, banks will need to use static haircuts rather than VaR modeling. Further, as proposed, the risk weighting for
broker/dealers will be 100%. The standardized haircut for an S&P 500 portfolio is anticipated to be 10.6%. So, in the above
example, the new RWA under the Collins Amendment would be as follows:
Exposure = (100,000,000* (1+.106)) - 102,000,000 = 8,600,000
If the borrower is a Broker/Dealer the RWA would also be $8,600,000.
Assuming the same target Capital/RWA and cost of capital assumptions as above, the new cost of the indemnity to the agent
lender would be $103,200, or 10.3 bps.
A capital cost of 10.3bps is approximately 45x the expected value of the indemnity to the beneficial owner, as measured by the
call option. Further, the net spread earned by agent lenders on many transactions today is less than 10.3 bps. Under the
methodology set forth under the new rules, therefore, indemnification of many easier-borrow, or lower spread, trades may be
harder to justify economically and perhaps ultimately may be cost prohibitive. If the latter proves true, collateral availability and
security pricing in the markets could be negatively impacted.
Summary
Beneficial owners and agent lenders have come to accept borrower default indemnification by the agent lender as the norm. The
emerging regulatory framework under Dodd Frank and Basel III, however, is expected to dramatically impact agent lender banks’
cost of capital calculations and required risk-weighted assets for indemnified loan transactions. Given the shifting cost/benefit
structure, the lending community will need to consider how indemnification may be provided in the future. With a mutual
understanding of its value and cost, lenders and their agents can better assess the optimal parameters for their lending
programs, including but not limited to right-sized loan balances, borrower diversification, potential minimum spread requirements
and shared revenues. State Street continues to participate in industry efforts to inform the rulemaking efforts of regulatory
agencies by responding to requests for comment and information. We welcome clients to join in this endeavor.
The information and charts containd herein are for illustrative purposes only. The views expressed in this material are the views of State Street
Securities Finance, through the period ended October 31, 2013, and are subject to change based on market and other conditions. This
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