IV.C. Performance Measurement and Attribution Flashcards
Suppose you purchase one share of the stock of Volatile Engineering Corporation at the beginning of year 1 for $36. At the end of year 1, you receive a $2 dividend, and buy one more share for $30. At the end of year 2, you receive total dividends of $4 (i.e., $2 for each share), and sell the shares for $36.45 each. The time-weighted return on your investment is ________.
Geometric mean is used to calculate the time-weighted return.
Geometric mean return = Rg = [(1 + R1)(1 + R2)….(1 + Rn)]1/n - 1
Year 1 = ($30 + $2 - $36)/$36 = - 11.11%
Year 2 = ($36.45 + $2 - $30)/$30 = 28.17%
Rg = [(0.8889)(1.2817)]1/2 - 1
Rg = 6.74%
You want to evaluate three mutual funds using the information ratio measure for performance evaluation. The risk-free return during the sample period is 6% and the average return on the market portfolio is 19%. The average returns, residual standard deviations, and betas for the FUND A is given:
Beta: 0.8
Residual SDEV: 4.00%
Avg Return: 20%
What is the information ratio of fund A?
A: P = [20] - [(6) + (.8(19 - 6))] = 3.6
3.6/4 = 0.9
They used CAPM to solve for alpha since beta was given for each. If they don’t give you beta on your exam, just subtract the risk-free from the fund or asset returns.
And remember that “residual standard deviation” is another name for tracking error.
One property of a risky portfolio that combines an active portfolio of mispriced securities with a market portfolio is that, when optimized, its squared Sharpe measure increases by the square of the active portfolio’s _______________.
Information Ratio
Consider the following probability distribution for stocks A and B:
State Probability Return on Stock A Return on Stock B
1 0.10 10% 8%
2 0.20 13% 7%
3 0.20 12% 6%
4 0.30 14% 9%
5 0.20 15% 8%
The coefficient of correlation between A and B is:
0.46
covA,B = 0.1(10% - 13.2%)(8% - 7.7%) + 0.2(13% - 13.2%)(7% - 7.7%) + 0.2(12% - 13.2%)(6% - 7.7%) + 0.3(14% - 13.2%)(9% - 7.7%) + 0.2(15% - 13.2%)(8% - 7.7%) = 0.76;
rA,B = 0.76/[(1.1)(1.5)] = 0.46.
Suppose two portfolios have the same average return, the same standard deviation of returns, but portfolio A has a lower beta than portfolio B. According to the Treynor measure, the performance of portfolio A __________.
is better/worse/the same as port B.
is better than the performance of portfolio B
Suppose you purchase 100 shares of Apple stock at the beginning of year 1 and purchase another 100 shares at the end of year 1. You sell all 200 shares at the end of year 2. Assume that the price of Apple stock is $50 at the beginning of year 1, $55 at the end of year 1, and $65 at the end of year 2. Assume no dividends were paid on Apple stock. Your dollar-weighted return on the stock will be __________ your time-weighted return on the stock.
higher than
In the dollar-weighted return, the stock’s performance in the second year, when 200 shares are held, has a greater influence on the overall dollar-weighted return. The time-weighted return ignores the number of shares held.
The following data are available relating to the performance of Longhorn Fund and the market portfolio:
Longhorn Market
Avg R 18% 14%
SDEV 30% 22%
Beta 1.4 1.0
Residual SDEV4.0% 0.0%
The risk-free return during the sample period was 6%.
If you wanted to evaluate the Longhorn Fund using the M2 measure, what percent of the adjusted portfolio would need to be invested in T-Bills?
Clearly you must use the formula for M2 to solve this one. You know that the first part of the M2 calculation is used for the value associated with the risk-free return. This is [1-(SDEVm/SDEVf)].
Thus, [1-(22/30)] = 26.67% in T-Bills
The Value Line Index is an equally weighted geometric average of the returns of about 1,700 firms. The value of an index based on the geometric average returns of 3 stocks where the returns on the 3 stocks during a given period were 32%, 5%, and -10%, respectively, is __________.
((1.32)(1.05)(0.90))1/3 - 1.0 = 7.6%
