LO 70.9: Describe and apply performance attribution procedures, including the asset allocation decision, sector and security selection decision, and the aggregate contribution.
William Sharpe introduced the concept of style analysis. From January 1985 to December 1989 he analyzed the returns on Fidelitys Magellan Fund for style and selection bets. His study concluded that 97.3% of the funds returns were explained by style bets (asset allocation), and 2.7% were due to selection bets (individual security selection and market timing). The importance of long-run asset allocation has been well established empirically. These results suggest that the returns to market timing and security selection are minimal at best and at worst insufficient to cover the associated operating expenses and trading costs.
The steps for Sharpes style analysis are as follows: 1. Run a regression of portfolio returns against an exhaustive and mutually exclusive set of
asset class indices:
Rp – bpiRB1 + bp2RB2 + …+ bpix^Bn + ep
where: Rp = return on the managed portfolio Rb- = return on passive benchmark asset class n bp. = sensitivity or exposure of Portfolio P return to passive asset class n return e = random error term
In Sharpes style analysis, the slopes are constrained to be non-negative and to sum to 100%. In that manner, the slopes can be interpreted to be effective allocations of the portfolio across the asset classes.
2. Conduct a performance attribution (return attributable to asset allocation and to
selection): The percent of the performance attributable to asset allocation = R2 (the coefficient
of determination).
The percent of the performance attributable to selection = 1 R2.
The asset allocation attribution equals the difference in returns attributable to active asset allocation decisions of the portfolio manager:
[biRgi + b2RB2 + …+ bnRgJ – Rg
Notice if the slopes (estimated allocations) for the managed portfolio equal those within the benchmark (passive asset allocation), then the asset allocation attribution will be zero.
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The selection attribution equals the difference in returns attributable to superior individual security selection (correct selection of mispriced securities) and sector allocation (correct over and underweighting of sectors within asset classes):
Rp
[bjRgj + b2RB2 + …+ bnRBn]
Notice if the manager has no superior selection ability, then portfolio returns earned within each asset class will equal the benchmark asset class returns: RPj = Rgj, and the selection attribution will equal zero. Also, notice that the sum of the two attribution components (asset allocation plus selection) equals the total excess return performance: Rp Rg.
3. Uncover the investment style of the portfolio manager: the regression slopes are used to infer the investment style of the manager. For example, assume the following results are derived:
Rp = 0.75Rl c g + 0.15Rl c v + 0.05Rs c g + 0.05RSCV
where: Rl c g = return on the large cap growth index Rpcy = return on the large cap value index Rsc g = return on the small cap growth index RSCv = return on the small cap value index
The regression results indicate that the manager is pursuing primarily a large cap growth investment style.
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Ke y Co n c e pt s
LO 70.1 The dollar-weighted rate of return is defined as the internal rate of return (IRR) on a portfolio, taking into account all cash inflows and outflows. The beginning value of the account is an inflow as are all deposits into the account. All withdrawals from the account are outflows, as is the ending value.
Time-weighted rate of return measures compound growth. It is the rate at which $ 1 compounds over a specified time horizon. Time-weighting is the process of averaging a set of values over time.
LO 70.2 The Sharpe ratio uses standard deviation (total risk) as the relevant measure of risk. It shows the amount of excess return (over the risk-free rate) earned per unit of total risk.
The Treynor measure is very similar to the Sharpe ratio except that it uses beta (systematic risk) as the measure of risk. It shows the excess return (over the risk-free rate) earned per unit of systematic risk.
Jensens alpha is the difference between the actual return and the return required to compensate for systematic risk. To calculate the measure, we subtract the return calculated by the capital asset pricing model (CAPM) from the account return.
The information ratio is the ratio of the surplus return (in a particular period) to its standard deviation. It indicates the amount of risk undertaken to achieve a certain level of return above the benchmark.
LO 70.3 The M2 measure compares the return earned on the managed portfolio against the market return, after adjusting for differences in standard deviations between the two portfolios.
LO 70.4 A positive alpha produces an indication of superior performance; a negative alpha produces an indication of inferior performance; and zero alpha produces an indication of normal performance matching the benchmark.
LO 70.3 Hedge fund performance evaluation is complicated because: Hedge fund risk is not constant over time (nonlinear risk). Hedge fund holdings are often illiquid (data smoothing). Hedge fund sensitivity with traditional markets increases in times of a market crisis and
decreases in times of market strength.
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LO 70.6 Changes in volatility will likely bias the Sharpe ratio, and produce incorrect conclusions when comparing portfolio performance to a benchmark or index.
LO 70.7
Extending basic return regression models offers a tool to assess superior market timing skills of a portfolio manager. A market timer will include high (low) beta stocks in her portfolio if she expects an up (down) market. If her forecasts are accurate, her portfolio will outperform the benchmark portfolio.
LO 70.8 William Sharpe introduced the concept of style analysis. From January 1985 to December 1989 he analyzed the returns on Fidelitys Magellan Fund for style and selection bets. His study concluded that 97.3% of the funds returns were explained by style bets (asset allocation), and 2.7% were due to selection bets (individual security selection and market timing).
LO 70.9 The importance of long-run asset allocation has been well established empirically. Historical results suggest that the returns to market timing and security selection are minimal at best and at worst insufficient to cover the associated operating expenses and trading costs.
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Topic 70 Cross Reference to GARP Assigned Reading – Bodie, Kane, and Marcus, Chapter 24
Co n c e pt Ch e c k e r s
Use the following data to answer Questions 1 and 2. Assume you purchase a share of stock for $50 at time t = 0 and another share at $65 at time t = 1, and at the end of year 1 and year 2, the stock paid a $2.00 dividend. Also at the end of year 2, you sold both shares for $70 each.
1.
2.
3.
The do liar-weighted rate of return on the investment is: A. 10.77%. B. 15.45%. C. 15.79%. D. 18.02%.
The time-weigh ted rate of return on the investment is: A. 18.04%. B. 18.27%. C. 20.13%. D. 21.83%. The following information is available for funds ABC, RST, JKL, and XYZ:
F und
A nnual Rate o f Return
ABC RST JKL XYZ
15% 18% 25% 11%
Beta 1.25 1.00 1.20 1.36
Volatility
20% 25% 15% 9%
The average risk-free rate was 5%. Rank the funds from best to worst according to their Treynor measure. A. JKL, RST, ABC, XYZ. B. JKL, RST, XYZ, ABC. C. RST, JKL, ABC, XYZ. D. XYZ, ABC, RST, JKL.
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Use the following information to answer Question 4. The following data has been collected to appraise funds A, B, C, and D:
Return Beta Standard deviation
F und A 8.25% 0.91 3.24%
F und B 7.21% 0.84 3.88%
F und C 9.44% 1.02 3.66%
F und D 10.12%
1.34 3.28%
M arket Index
8.60% 1.00 3.55%
The risk-free rate of return for the relevant period was 4%.
4.
5.
Calculate and rank the funds from best to worst using Jensens alpha. A. B, D, A, C. B. A, C, D, B. C. C,A, D, B. D. C, D, A, B.
Sharpes style analysis, used to evaluate an active portfolio managers performance, measures performance relative to: A. a passive benchmark of the same style. B. broad-based market indices. C. D. an average of similar actively managed investment funds.
the performance of an equity index fund.
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Co n c e pt Ch e c k e r An s w e r s 1. D One way to do this problem is to set up the cash flows so that the PV of inflows = PV of
outflows and then to plug in each of the multiple choices.
50 + 65 / (1 + IRR) = 2 / (1 + IRR) + 144 / (1 + IRR)2 -> IRR = 18.02%
Alternatively, on your financial calculator, solve for IRR: -50 – + IRR 6 5 -2 ———- b 1 + IRR
2(70 + 2) (l + IRR)2
Calculating Dollar- Weighted Return With the TI Business Analyst II Plus
Key Strokes [CF] [2nd] [CLR WORK] 50 [+/-] [ENTER] [4] 63 [+/-] [ENTER] [4-] [4-] 144 [ENTER] [IRR] [CPT]
Explanation Clear CF Memory Registers Initial cash inflow Period 1 cash inflow Period 2 cash outflow Calculate IRR
Display CFO = 0.00000 CFO = -50.00000 C01 =-63.00000 C02 = 144.00000 IRR = 18.02210
2. D HPR, = (65 + 2) / 50 – 1= 34%, HPR, = (140 + 4) / 130 – 1 = 10.77%
time-weighted return = [(1.34)(1.1077)]0’5 1 = 21.83%.
3. A Treynor measures:
^ n T ARr = —————= 0.08 = 8 a b c
0.15-0.05
_
L
2
3
0.18-0.05 _ Tr st = ————- – = 0.13 = 13 R S T
1.00
0.25-0.05
1.20
0.11-0.05
1.36
= 0.1667 = 16.7
= 0.0441 = 4.4
The following table summarizes the results:
Fund ABC RST JKL XYZ
Treynor Measure
Rank
8.00% 13.00% 16.67% 4.41%
3 2 1 4
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4. C CAPM Returns:
Ra = 4 + 0.91(8.6-4) = 8.19% RB = 4 + 0.84(8.6 – 4) = 7.86% Rc = 4 + 1.02(8.6-4) = 8.69% Rd = 4+ 1.34(8.6-4) = 10.16%
F und A
F und B
F und C
F und D
Alpha
8.25% -8.19%
= +0.06
Ranking
2
7.21% -7.86%
9.44% – 8.69%
= -0.65%
4
= +0.75%
1
10.12% – 10.16%
= -0.04%
3
5. A Sharpes style analysis measures performance relative to a passive benchmark of the same
style.
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The following is a review of the Risk Management and Investment Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
H e d g e Fu n d s
Ex a m Fo c u s
Topic 71
The topic examines two decades of hedge fund performance. Significant events that shaped the hedge fund industry are discussed, including the growth of institutional investments. Different hedge fund strategies are explained, along with the continuing growth of assets under management. Performance is analyzed to see if the rewards justify the risks, and performance is compared with the broad equity markets. The performance of top fund managers is also compared to the performance across the hedge fund industry.
C h a r a c t e r is t ic s o f H e d g e Fu n d s