Available online at www.sciencedirect.com
Electrical Power and Energy Systems 29 (2007) 803–809
www.elsevier.com/locate/ijepes
Quantifying price risk of electricity retailer based on CAPM
and RAROC methodology
R.G. Karandikar *, S.A. Khaparde, S.V. Kulkarni
Electrical Engineering Department, Indian Institute of Technology Bombay, Mumbai 400 076, India
Received 7 August 2006; received in revised form 10 June 2007; accepted 17 June 2007
Abstract
In restructured electricity markets, electricity retailers set up contracts with generation companies (GENCOs) and with end users to
meet their load requirements at agreed upon tariff. The retailers invest consumer payments as capital in the volatile competitive market.
In this paper, a model for quantifying price risk of electricity retailer is proposed. An IEEE 30 Bus test system is used to demonstrate
the model. The Capital Asset Pricing Model (CAPM) is demonstrated to determine the retail electricity price for the end users. The factor
Risk Adjusted Recovery on Capital (RAROC) is used to quantify the price risk involved. The methodology proposed in this paper can be
used by retailer while submitting proposal for electricity tariff to the regulatory authority.
2007 Elsevier Ltd. All rights reserved.
Keywords: CAPM; RAROC; Electricity retailer
1. Introduction
The restructured power sector has caused electricity to
be a market commodity. These markets are classified as
physical market or financial market [1]. The retailer enters
in contract with GENCOs in this open market. Entering
such contract the electricity retailer commits himself to
the obligation to purchase and deliver electricity at an
agreed upon price. Hence, one must quantify the price risk
related to such electricity retailer contracts. Unlike the
retailers for the other types of commodities the electricity
retailer have very limited role but they are required to provide value added services to the consumers. They are the
financial intermediary who acquires the electricity from
the GENCOs and resell it to different types of consumers.
Providing future load requirements accurately to the suppliers is an integral part of these supply contracts. In [2]
*
Corresponding author. Tel.: +91 22 25722545/25764424; fax: +91 22
2572 3707.
E-mail addresses: [email protected] (R.G. Karandikar), [email protected].
ac.in (S.A. Khaparde), [email protected] (S.V. Kulkarni).
0142-0615/$ - see front matter 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijepes.2007.06.007
the analysis of retailer’s strategies for determining forward
loads is demonstrated. A framework for comparing and
analyzing price risk for electricity retailers is presented in
[3]. Financial institutions use Value at Risk (VaR) analysis
for portfolio management. In [4] application of this
approach in case of restructured electricity markets of
‘‘Tasmania’’ is demonstrated.
In restructured environment, the open access encourages
the private entities to invest in generation. The Schedule
Coordinator (SC) coordinates the generation by submitting
offer in bilateral transactions with the Grid. In [5] a bidding
scheme is proposed based on the actual cost of generation
to minimize risk in profit of such generation companies.
The generation companies need to do optimal bidding in
day-ahead power markets to maximize their profit. A
robust method for self-scheduling of such generation companies based on VaR is discussed in [6]. This methodology
is used to reduce the risk resulting from exposure to fluctuating local marginal prices. In [7] the risks of the energy service company (ESCO) are identified and the contract
specifications and the VaR are evaluated. In [8] technoeconomical model of an electric energy service provider
in Spain is proposed.
804
R.G. Karandikar et al. / Electrical Power and Energy Systems 29 (2007) 803–809
If asset returns are positively correlated, portfolio variance increases and if asset returns are negatively correlated
then it reduces portfolio risk. The total portfolio risk can be
thought of as the sum of systematic and unsystematic risks.
A capital asset pricing model (CAPM) is a simple relationship that links the return on particular stock with the return
on portfolio made up of the entire market [9]. The CAPM
model is widely used as measure of risk in the portfolio
investment. The model can be appropriately used for electricity retailers who invest the payment (capital) received
from end users in GENCOs in competitive market.
Different portfolio management techniques are used to
quantify the risk in case of electricity markets. An application of efficient frontier, one of the portfolio management
tools to assess the risk associated in expected payoff of
GENCOs is presented in [10,11]. The upcoming challenge
for researchers in electricity market is to quantify the risk
associated in case of various market participants. The
RAROC (Risk Adjusted Return on Capital) methodology,
most commonly used financial risk measure is discussed in
[12,13]. The use of RAROC methodology to develop Monte
Carlo Simulation based model to quantify risks related to
electricity contracts of retailers is presented in [14].
In this paper, the Capital Asset Pricing Model (CAPM)
is demonstrated to determine the retail electricity price for
the end users. The factor Risk Adjusted Recovery on Capital (RAROC) is used to quantify the price risk involved.
The IEEE 30 Bus test system is used to demonstrate the
results [15]. The rest of the paper is organized as follows:
In Section 2 fundamentals of CAPM and RAROC
approach are discussed. The formulation and results are
given in Section 3. The main conclusions of this work are
summarized in Section 4.
2. CAPM and RAROC methodology
2.1. Capital Asset Pricing Model (CAPM)
CAPM model is basically applied to the portfolio investment in security market. In finance, the CAPM model
applied with assumption that for a particular capital how
and in what proportion the investor should invest in portfolios so that the returns are maximized. In electricity market the retailer purchase electricity in the market and its
price risk is influenced by the behaviour of market participant, network constraints and load. The capital of retailer
depends on load and consumer price. For maximum
returns the consumer price i.e. capital generation of retailer
should be adequate and optimum. Hence, while deciding
consumer tariff or while giving tariff proposals to regulator,
retailer can use CAPM model as a guideline.
The CAPM is one of the models in investment modelling. It addresses to reasonable price for an asset. The
investor in such case gets returns (profit) depending upon
variation in the asset prices. The risk involved in such
investment is quantified in terms of variance and for any
such fund (capital) total variance of the return must be
minimized. Prices of assets under heavy demand will go
up and prices of assets under light demand will go down.
The price changes will affect the estimates of asset returns.
Therefore, investors will recalculate their optimal portfolios. The process continues until demand matches supply;
that is, until there is an equilibrium. If the market portfolio
is efficient, then the expected return E{ri} of any asset i satisfies Eq. (1). The (E{ri rf}) is called the Expected Excess
Rate of Return of asset i. It indicates the amount by which
the rate of return exceeds the risk-free rate. The
(E{rm} rf) is called the Expected Excess Rate of Return
of the market portfolio.
Eðri Þ ¼ bi ðEðrm Þ rf Þ þ rf
ð1Þ
where
ri;m
bi ¼ 2
rm
bi is normalised covariance between ith asset and total
portfolio returns:
rf is risk free rate of return
rm is rate of market return
The CAPM model depicts that the expected excess rate
of return of an asset is proportional to the expected excess
rate of return of the market portfolio and the constant
of proportionality factor is b, which is given by bi ¼
ri;m =r2m . The bi is a normalized version of the co-variance
of an asset with respect to the market portfolio. The excess
rate of return for an asset is directly proportional to its covariance with the market.
The aggressive assets/companies or highly leveraged
companies have high betas and on the other hand, conservative companies whose performance is unrelated to the general market behaviour are expected to have low betas. If
b = zero then the asset is completely uncorrelated with the
market. In such case as per the CAPM model, the E{r} will
be rf. Even if the asset is risky, its expected rate of return is
the risk-free rate. There is no premium for risk with large
covariance. In such case, the risk must be diversified by
using proper strategy while investing. If b < 0, then
E{r} < rf and the asset may have very high risk (as measured
by its r) and expected rate of return will be even less than the
risk-free rate. Such an asset reduces the overall portfolio risk
when combined with the market. In such case, the investors
are willing to accept the lower expected value for this riskreducing potential. Such assets provide a form of insurance.
The CAPM model has different concept of quantifying
the risk of an asset from r to b. In the proposed methodology, the CAPM model is applied to the electricity market.
The electricity retailer gets payments from the consumer,
which he invests as a capital in different GENCOs. The
capital depends on the market price, load and the consumer per unit price of electricity (all other costs not taken
into account). The retailer can quantify the risk in his business by applying CAPM model for the different per unit
prices (tariff).
R.G. Karandikar et al. / Electrical Power and Energy Systems 29 (2007) 803–809
In the proposed work, per unit price is determined based
on the CAPM model and risk quantification is done using
RAROC factor.
distribution. Thus, the RAROC for an electricity retailer
becomes
Expected profit
CFaRa
E½profit
RAROC ¼
E½profit qa ½profit
RAROC ¼
2.2. Risk adjusted recovery of capital (RAROC)
RAROC, a risk quantifying factor, is defined as the
ratio of expected return and economic capital (EC). The
EC is the amount of money, which is needed to secure
the investor’s survival in worst-case scenario. EC captures
all types of risk and often calculated as Value at Risk
(VaR). The VaR is quantile of the profit and loss (P and
L) distribution. It measures the maximum amount of
money one can lose at given confidence level in specified
period. In case of banking, VaR is widely used to quantify
risk. However, in case of electricity markets VaR is not an
appropriate measure of risk because when VaR is used, it is
implicitly assumed that it is possible to close the risky position at any time in future or forward market. This is not
practically possible in case of electricity markets. Hence,
better approach to quantify risk is Cash Flow at Risk
(CFaR) than VaR. The VaR is based on the future
prices and on the other hand, CFaR is based on the spot
prices.
The electricity retailers buy electricity in the spot market
from GENCOs for which they invest return (capital) generated out of consumer payment. The traditional performance measures to evaluate the performance of an
investment company are mainly RoI – Return on Investment and RoE – Return on Equity. RoI compares the
return to the amount of invested money; on the other hand,
RoE considers only the invested equity capital.
RoI ¼
Return
Invested capital
Return
RoE ¼
Invested equity capital
805
ð3Þ
ð4Þ
The a-quantile is the loss that will occur at given probability level (Fig.1). For to calculate a-quantile normal distribution of profit and loss vector is plotted as shown in
Fig. 1. Once we get the value of loss from the normal distribution, we can calculate value of the loss using the average and standard deviation of profit/loss vector.
Let the consumer’s fixed retail price be k, the deterministic load at hour h is Pdh, total generation is Pgh and the
stochastic spot price of 1 MW h at hour h be Market Clearing Price MCPh. Then the profit for each hour is the difference between the retail and the spot price per MW h times
the amount of energy. Let the cash flow in hour h be Prh
and since MCPh is stochastic, Prh is stochastic.
E½P rh ¼ E½kP dh MCP h P gh ð5Þ
To get the entire profit, calculate a sum over all hours
from the starting hour s of the contract until the end hour
T and discount the cash flows to the actual point in time i.e.
hour, denoted as hour h0. For simplicity, if we take constant risk free interest rate r with continuous compounding
then the profit function of retailer is given by;
"
#
T
X
rðhsÞ
E½profit ¼ E
e
P rh
"
¼E
h¼s
T
X
e
rðhh0 Þ
E ððkÞðP ht ÞÞ ððMCPh ÞðP gh ÞÞ
#
h¼s
ð6Þ
ð2Þ
The shortcomings of these concepts are (1) they are
accounting-based and do not reflect the real performance
(2) neither do they consider risk nor is it possible to determine the denominator for single business units from the
firm’s balance sheet. The RoI, RoE and similar measures
do not consider risk. Suppose there are two investments,
both have the same rate of return but one of them can be
much riskier. Therefore, the return has to be compared
to the risk undertaken. Otherwise, it will be impossible to
compare the performances of two different investments or
business units. There is a need of an efficient risk management and the ability to compare different business unit’s
Risk. The Risk Adjusted Performance Measures (RAPMs)
are being used in the banking business.
The Economic Capital ensures enough capital for the
survival in worst case. As explained previously CFaR
rather than VaR should be used to determine the Economic
Capital. The relative CFaR is defined as the difference
between the mean and the a-quantile of the profit and loss
Using Eq. (6) one can calculate the profit i.e. the sum of
all cash flows at every hour. The risk factor RAROC is
determined to quantify risk in rate of return.
3. Formulation and results
Even though the prices in the competitive market are
volatile, most of the times the retailer charges to end user
at fixed rates. The normal trend is to charge consumer at
Fig. 1. Normal distribution.
806
R.G. Karandikar et al. / Electrical Power and Energy Systems 29 (2007) 803–809
average price but it does not mean for this price the retailer’s business is optimum and at minimum price risk.
Hence, there is need of proper methodology based on
which the retailer company can estimate non-discriminative fixed price. The assumption made while developing
model is flat rate tariff for consumer and the distribution
charges, taxes, ancillary service charges and other charges
are not taken into consideration.
3.1. Test system
IEEE 30 bus test system is used and MATPOWERTM is
used to get OPF solution for given load, generator data,
and other network constraints [15]. The cost curve constants
of six generators are given in Table 1.
The load at different buses is varying hour to hour. The
total average load assumed on the 30 Bus systems is
181.31 MW, the maximum is 217 MW and the minimum
is 127.04 MW. Fig. 2 gives the total load variation for
the 334 h (2 weeks).
For different per hour load condition the OPF is run.
Table 2 summarizes the marginal generation costs of six
generators and the highest marginal generation cost is
MCP. The average MCP is $153.68, the maximum is
$262.5 and the minimum is $82.68.
Bus no.
1
2
6
3
5
4
1
2
13
22
23
27
a
b
0.02
0.0175
0.025
0.0625
0.025
0.0834
2.0
1.75
3.5
1.0
3.0
3.25
210
200
190
180
MW 170
160
150
140
130
120
100
3.3. CAPM model
3.3.1. Model description
The quantification of business of the Retailer Company
and determination of consumer price is done using CAPM
model. The capital of retailer is consumer payment which is
dependent on load and consumer price. The consumer
price can be the average price in given time horizon. But
it cannot be very high in regulated market as consumer welfare is a main concern of market regulator. The expected
rate of return of retailer from one generator is determined
using CAPM model is as follows
ð7Þ
where
Load (MW)
50
• Using load and system data run OPF and get set of generation schedule for six generators and marginal prices
of generators.
• Set the maximum marginal price as MCP for that hour.
• Repeat the above procedure for all 334 h. (Assumed
time horizon in present case)
• Determine the non-discriminative consumer price using
CAPM and quantify price risk using risk factor
RAROC.
PG cost ðap2g Þ + (bpg)
220
0
The algorithm used for the solution is as follows
Eðrg Þ ¼ bðEðrm Þ rf Þ þ rf
Table 1
Generator cost curve constants
Sr. no.
3.2. Algorithm
150
200
250
Hour
Fig. 2. Load data for 334 h.
300
350
E(rg) = expected rate of return from generator
rf = risk free rate of return
E(rm) = expected rate of market return of each portfolio
i.e. each generator and is a ratio of generator mean
profit and mean of total profit.
b = normalized co-variance between profit form generator and total profit of retailer.
3.3.2. Results
For different per unit prices (150–168 $/MW h), rate of
return for each generator, b and average rate of return
from generators are determined. From (7), the generator
rate of return is dependent on the b, rm and on assumed
risk free rate of return. In present case, risk free rate of
return is assumed 4%, 6% and 8% (refer Table 3–5).
The average rate of return compared to risk free rate
must be independent of the risk free rate assumed. From
the results tabulated it is implicated that for the price of
161.22$/MW h the average rate of return is maximum
and is independent of risk free rate of return. For the retailer price of 161.22$/MW h the rate of return from GENCOs is maximum. Thus, for the price 161.22$/MW h,
CAPM model gives best rate of asset returns for the portfolio (GENCOs) in which the retailer company invests its
payment (capital) received form consumer. Tables 3–5 give
the expected rate of return and b for different prices.
R.G. Karandikar et al. / Electrical Power and Energy Systems 29 (2007) 803–809
807
Table 2
Cost of generation and MCP
Cost of generation ($/MW h)
hr. 1
hr. 2
:
hr. 300
hr. 334
Generator at bus 1
Generator at bus 2
Generator at bus 13
Generator at bus 22
Generator at bus 23
Generator at bus 27
MCP ($/MW h)
Average MCP is $153.68
78.00
98.00
78.25
29.90
103.03
88.87
103.03
78.00
98.00
89.24
40.59
119.09
118.95
119.09
:
:
:
:
:
:
:
130.5
114.1875
109.5472
168.6949
36.5417
218.5499
218.5499
130.5
114.18
81.79
34.87
111.74
96.63
130.5
Table 3
b of different generators and price and expected return of retailer from each generator (rf = 4%)
Price $/MW h
b1
b2
b3
b4
b5
b6
E(rg1)
E(rg2)
E(rg3)
E(rg4)
E(rg5)
E(rg6)
Ave. E(rg)
150
152
154
156
158
160
160.5
161.22a
161.26
161.3
162
164
168
0.2574
0.2564
0.2554
0.2544
0.2533
0.2523
0.252
0.2516
0.2516
0.2516
0.2512
0.2501
0.2479
0.271
0.2698
0.2686
0.2674
0.2662
0.2649
0.2646
0.2642
0.2641
0.2641
0.2637
0.2624
0.2598
0.1463
0.1468
0.1473
0.1478
0.1483
0.1488
0.1489
0.1491
0.1491
0.1491
0.1493
0.1498
0.1508
0.0648
0.0646
0.0644
0.0642
0.0640
0.0638
0.0637
0.0637
0.0637
0.0637
0.0636
0.0634
0.0630
0.1154
0.1166
0.1178
0.1189
0.1201
0.1213
0.1216
0.1221
0.1221
0.1221
0.1225
0.1238
0.1262
0.123
0.123
0.124
0.124
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.126
0.127
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.031
0.031
0.031
0.031
0.031
0.031
0.03
0.03
0.03
0.03
0.03
0.03
0.031
0.029
0.029
0.029
0.03
0.03
0.03
0.0342
0.0342
0.0341
0.034
0.0338
0.0327
0.0312
0.0421
0.0409
0.0399
0.0359
0.0348
0.0344
0.0374
0.0375
0.0375
0.0375
0.0375
0.0374
0.0374
0.0377
0.0377
0.0376
0.0375
0.0375
0.0375
0.0354
0.0353
0.0352
0.035
0.0347
0.0334
0.0315
0.0449
0.0434
0.0422
0.0373
0.0359
0.0354
0.0352
0.0351
0.0351
0.035
0.0348
0.0341
0.033
0.0406
0.0397
0.0391
0.0363
0.0355
0.0353
0.0337
0.0337
0.0337
0.0337
0.0336
0.033
0.0323
0.0376
0.037
0.0366
0.0346
0.0341
0.0339
a
For the price of 161.22$/MW h the average rate of return is maximum.
Table 4
b of different generators and price and expected return of retailer from each generator (rf = 6%)
Price $/MW h
b1
b2
B3
b4
b5
b6
E(rg1)
E(rg2)
E(rg3)
E(rg4)
E(rg5)
E(rg6)
Ave.E(rg)
150
152
154
156
158
160
160.5
161.22a
161.26
161.3
162
164
168
0.2575
0.2565
0.2555
0.2545
0.2534
0.2524
0.2521
0.2517
0.2517
0.2517
0.2513
0.2502
0.2480
0.2711
0.2700
0.2688
0.2675
0.2663
0.2651
0.2647
0.2643
0.2643
0.2642
0.2638
0.2625
0.2599
0.1464
0.1469
0.1474
0.1479
0.1484
0.1489
0.1490
0.1492
0.1492
0.1492
0.1494
0.1499
0.1510
0.0649
0.0647
0.0645
0.0643
0.0641
0.0639
0.0638
0.0637
0.0637
0.0637
0.0637
0.0635
0.0631
0.1155
0.1166
0.1178
0.1190
0.1202
0.1214
0.1217
0.1221
0.1221
0.1222
0.1226
0.1238
0.1263
0.1230
0.1234
0.1238
0.1242
0.1246
0.1250
0.1251
0.1253
0.1253
0.1253
0.1255
0.1259
0.1268
0.045
0.045
0.045
0.045
0.045
0.045
0.045
0.046
0.046
0.046
0.045
0.045
0.045
0.044
0.044
0.044
0.044
0.044
0.045
0.045
0.043
0.043
0.044
0.044
0.044
0.045
0.0513
0.0513
0.0512
0.0511
0.0508
0.0497
0.0482
0.0591
0.0578
0.0569
0.0529
0.0518
0.0514
0.0561
0.0562
0.0562
0.0562
0.0562
0.0562
0.0561
0.0564
0.0564
0.0564
0.0563
0.0562
0.0563
0.0531
0.0530
0.0528
0.0527
0.0523
0.0510
0.0490
0.0624
0.0609
0.0597
0.0548
0.0534
0.0529
0.0527
0.0527
0.0526
0.0525
0.0523
0.0516
0.0505
0.0580
0.0571
0.0565
0.0538
0.0530
0.0527
0.0505
0.0505
0.0504
0.0504
0.0503
0.0498
0.0490
0.0543
0.0537
0.0533
0.0514
0.0508
0.0507
a
For the price of 161.22$/MW h the average rate of return is maximum.
3.4. RAROC factor
3.4.1. Methodology to determine RAROC factor
The retailer’s capital is the payment he receives from
load at fixed retailer price. He invests this capital in the
generation companies. In the present model, he invests in
six-generation companies. The generation companies are
paid at MCP, which is volatile spot price. Thus, the retailer’s profit (expected return) is stochastic. Fig. 3 gives the
variation of MCP compared to the average MCP of
$153.68.
To get the entire profit earned in the 334 h we just have
to sum over all hours from the starting hour h0 until the
334th hour. Discount the cash flows to the actual point
of time, which is hour one. In the present case, we have
assumed constant risk free interest rate rf (4%, 6%, and
8%) with continuous compounding. The a-quantile is
determined using standard MATLABTM function. For all
334 hours different consumer price is assumed, say $150,
$152 and so on. The prices assumed are relative to the average price of $153.68 for assumed data and time horizon.
For very low prices compared to average price, the
808
R.G. Karandikar et al. / Electrical Power and Energy Systems 29 (2007) 803–809
Table 5
b of different generators and price and expected return of retailer from each generator (rf = 8%)
Price $/MW h
b1
b2
b3
b4
b5
b6
E(rg1)
E(rg2)
E(rg3)
E(rg4)
E(rg5)
E(rg6)
Ave.E(rg)
150
152
154
156
158
160
160.5
161.22a
161.26
161.3
162
164
168
0.2577
0.2566
0.2556
0.2546
0.2535
0.2525
0.2522
0.2518
0.2518
0.2518
0.2514
0.2503
0.2481
0.2713
0.2701
0.2689
0.2677
0.2664
0.2652
0.2649
0.2644
0.2644
0.2643
0.2639
0.2626
0.2600
0.1465
0.1469
0.1474
0.1479
0.1484
0.1490
0.1491
0.1493
0.1493
0.1493
0.1495
0.1500
0.1510
0.0649
0.0647
0.0645
0.0643
0.0641
0.0639
0.0638
0.0638
0.0638
0.0638
0.0637
0.0635
0.0631
0.1155
0.1167
0.1179
0.1190
0.1202
0.1214
0.1217
0.1222
0.1222
0.1222
0.1226
0.1239
0.1263
0.123
0.123
0.123
0.124
0.124
0.125
0.125
0.125
0.125
0.125
0.125
0.126
0.126
0.060
0.060
0.060
0.060
0.060
0.060
0.060
0.061
0.061
0.061
0.060
0.060
0.060
0.059
0.059
0.059
0.059
0.059
0.059
0.059
0.058
0.058
0.058
0.059
0.059
0.059
0.068
0.068
0.068
0.068
0.067
0.066
0.065
0.076
0.074
0.073
0.069
0.068
0.068
0.0748
0.0749
0.0749
0.0749
0.0749
0.0749
0.0749
0.0751
0.0751
0.0751
0.0750
0.0750
0.0750
0.0708
0.0706
0.0705
0.0703
0.0699
0.0685
0.0666
0.0799
0.0783
0.0772
0.0724
0.0710
0.0704
0.0702
0.0702
0.0701
0.0700
0.0698
0.0691
0.0680
0.0754
0.0746
0.0740
0.0713
0.0705
0.0702
0.0672
0.0672
0.0672
0.0671
0.0670
0.0665
0.0658
0.071
0.0704
0.0700
0.0681
0.0676
0.0674
a
For the price of 161.22$/MW h the average rate of return is maximum.
RAROC is determined using
Variation of MCP as compared to average price
Price ($/MWh)
300.00
RAROC ¼
250.00
200.00
Constant consumer
price
150.00
MCP
100.00
50.00
0.00
1
38 75 112 149 186 223 260 297 334
Hours
Fig. 3. Variation of MCP compared to average MCP of $153.68.
RAROC is low and less than unity. For each price for
entire 334 h expected return (profit), VaR and the factor
RAROC are determined. For the risk free rate of return
8%, the discounted profit over 334 h is given by,
"
#
334
X
ð0:08=8760Þðh0Þ
E½profit ¼ E
e
P rh
"
¼E
h¼0
334
X
e
ð0:08=8760Þðh0Þ
E ððkÞP dh Þ ðMCP h ÞP gh
#
h¼0
ð8Þ
Expected profit
E½profit
¼
CFaRa
E½profit qa ½profit
ð9Þ
3.4.2. Results
Table 6 gives the profit, Value at Risk (VaR), average
profit and RAROC factor for different consumer prices.
When the consumer price is $161.22 the risk-adjusted
return for retailer is maximum.
The profit, Value at Risk (VaR), average profit and
RAROC for different consumer prices and risk free rate
are given in Table 6. The risk factor RAROC is optimal
when retailer price is 161.22$/MW h.
4. Discussion
There are other financial tools used to quantify the
financial performance of the business. Cost-benefit analysis
(CBA), traditionally used technique, typically involves the
concept of time value of money. This is usually done by
converting the future expected costs and benefits to a present value. In order to calculate the present value of money,
Table 6
Profit, Value at Risk (VaR), average Profit and RAROC for different consumer prices and risk free rate
Price $/MW h
Risk free rate rf = 4%
Profit
VaR
Ave. profit
RAROC
Profit
VaR
Ave. profit
RAROC
Profit
VaR
Ave. profit
RAROC
150
152
154
156
158
160
160.5
161.22
161.26
161.3
162
164
168
666450
545450
424440
303430
182420
61409
31156
12407
14827
17248
59601
180610
422630
14372
13957
13541
13126
12711
12296
12193
12043
12035
12027
11882
11467
10639
1995.4
1633.1
1270.8
908.46
546.16
183.86
93.28
37.147
44.393
51.639
178.45
540.75
1265.4
0.9788
0.9750
0.9690
0.9585
0.9348
0.8331
0.7187
34.096
5.31
3.3036
1.249
1.0678
1.0258
666060
545100
424140
303170
182210
61249
31008
12538
14957
17377
59713
180680
422600
14366
13950
13535
13120
12705
12290
12187
12038
12029
12021
11876
11462
10634
1994.2
1632
1269.9
907.7
545.5
183.3
92.83
37.53
44.78
52.02
178.7
540.9
1265.3
0.97889
0.97505
0.96907
0.95852
0.93482
0.83287
0.71787
25.05
5.1083
3.2446
1.2483
1.0677
1.0258
665660
544750
423830
302920
182000
61089
30860
12669
15087
17506
59826
180740
422570
14359
13944
13529
13114
12699
12285
12181
12032
12024
12015
11870
11456
10629
1993
1631
1269
906.9
544.9
182.9
92.39
37.93
45.17
52.41
179.12
541.14
1265.2
0.1
0.9750
0.9690
0.9585
0.9347
0.8325
0.7169
19.886
4.9246
3.1885
1.2475
1.0677
1.0258
Risk free rate rf = 6%
Risk free rate rf = 8%
R.G. Karandikar et al. / Electrical Power and Energy Systems 29 (2007) 803–809
risk free rate is taken as reference to estimate the returns on
the investment.
The important cost-benefit indicators are (1) Present
Value of benefits (PVB), (2) Present value of Cost (PVC),
(3) Net Present Value (NPV), which is difference between
PVB and PVC, and (4) Benefit to Cost Ratio (BCR). The
BCR is also interpreted as the ratio of return on investment
(ROI). If there are number of profit making units under
one business unit, the CBA does not take into account rate
of returns from individual profit making units and rather it
takes into account returns of overall business unit. It also
does not take into account risk in returns apart from
accounting returns based on the risk free rate to calculate
present value.
The shortcomings of CBA are (1) they are accountingbased and do not reflect the real performance (2) neither
do they consider risk. The RAROC factor, which is also
based on the risk free return rate, (defined in Section 2.2)
takes into account the Value at Risk i.e. while calculating
the returns the worst possible loss in returns is taken into
account. In this respect the RAROC is better option from
the risk in the returns point of view. In the era of restructuring, the retailers are involved in the financial transactions with multiple GENCOs via bilateral contracts
which make it essential to value the business of retailer
for returns point of view from each GENCO. The CAPM
model (defined in Section 2.1), is also based on the comparing returns with reference to the risk free rate. The CAPM
gives rate of returns of retailer form the each individual
GENCO which is necessary while going for bilateral
contracts.
Finally, the retailer’s business is quantified from both
the return on investment point of view and the risk on
returns which is one of the unique feature of the methodology proposed in this paper (refer Tables 3–6).
5. Conclusion
In certain market mechanisms, the retailers get fixed rate
of return, subject to regulator approval, while they purchase the power at volatile market clearing prices. Work
presented in this paper helps the retailers in deciding their
quotes for the retail price of the consumers, under this market structure. In this case, the volatile energy prices are not
reflected on the consumer side and hence, price risk
involved in retail business is high.
Rate of return for the retailer’s business is calculated
using CAPM model. The risk on returns is quantified using
RAROC factor. The VaR parameter is also monitored for
the retailer which is further useful for risk quantification.
809
Thus, the use of the above tools can provide a guideline
for retailers to quote, and regulators to fix the consumer
tariff.
Acknowledgements
The authors are with Power Electronics and Power System Group, Department of Electrical Engineering, Indian
Institute of Technology, Bombay, 400076, India (e-mail:
[email protected], [email protected], [email protected]). The
authors would like to thank Ministry of Human Resource
Development, Government of India for their support
in carrying out this research work (Project No. F.2716/2003.TS.V).
References
[1] Stoft S. Power system economics: designing markets for electricity. New York: Wiley Interscience; 2002.
[2] Gabriel SA, Genc MF, Balakrishnan S. A simulation approach to
balancing annual risk and reward in retail electrical power markets.
IEEE Trans Power Syst 2002;17 (4).
[3] Ojanen OJ, Comparative analysis of risk management strategies for
electricity retailer. Master’s thesis, Helsinki Univ. of Technology,
Dept. Engineering and Mathematics, Finland; 2002.
[4] Moran A. Expectations for a competitive retail market in Tasmania.
Utilicon TasPower conference, April 2002.
[5] Kulkarni SV, Khaparde SA, Karandikar RG. Strategic optimal
bidding by schedule coordinator for distributed generators in
deregulated power system. Power systems 2003: distributed generation and advanced metering, March 12–14, Clemson USA; 2003.
[6] Jabr RA. Robust self-scheduling under price uncertainty. IEEE Trans
Power Syst 2005;20 (4).
[7] Shebl’e GB, Berleant D. Bounding the composite value at risk for
energy service company operation with DEnv, an interval-based
algorithm, Department of Electrical and Computer Engineering,
Iowa State University, USA.
[8] Yusta JM, Rosado IJR, Navarro JAD, Vidal JMP. Optimal
electricity price calculation model for retailers in a deregulated
market. Int J Electr Power Energ Syst 2005;27:437–47.
[9] Hull JC. Options, futures, and other derivatives. Singapore: Pearson
Education; 2003.
[10] Risk assessment and financial management, IEEE Tutorial, 1999.
[11] Karandikar RG, Abhyankar AR, Khaparde SA, Nagaraju P.
Assessment of Risk involved with bidding strategies of a Genco in
a day ahead market, Int J Emerging Electr Power Syst, The Berkeley
Electronic Pres 1 (1) (2004) Article 1006.
[12] Stoughton NM, Irvine UC, Zechner J. Optimal capital allocation
using RAROC and EVAR. Univ. of Vienna, November 2003.
[13] Hallerbach WG, Capital Allocation, portfolio enhancement and
performance measurement: a unified approach. EURO WGFM 2001,
Haarlem NL, Sydney, AUS., November 15, 2001.
[14] Prokopczuk M, Rachev S, TrÄuck S. Quantifying risk in the
electricity business: a RAROC-based approach, Univ. Karlsruhe
Kollegium am Schloss, Karlsruhe, Germany, October 11, 2004.
[15] Available online: www.pserc.cornell.edu/matpower.