Kelli Blakely is a portfolio manager for the Miranda Fund, a core large-cap equi
ID: 2795780 • Letter: K
Question
Kelli Blakely is a portfolio manager for the Miranda Fund, a core large-cap equity fund. The market proxy and benchmark for performance measurement purposes is the S&P 500. Although the Miranda portfolio generally mirrors the asset class and sector weightings of the S&P, Blakely is allowed a significant amount of leeway in managing the fund. However, her portfolio holds only stocks found in the S&P 500 and cash.
Blakely was able to produce exceptional returns last year (as outlined in the table below) through her market timing and security selection skills. At the outset of the year, she became extremely concerned that the combination of a weak economy and geopolitical uncertainties would negatively impact the market. Taking a bold step, she changed her market allocation. For the entire year her asset class exposures averaged 50% in stocks and 50% in cash. The S&P’s allocation between stocks and cash during the period was a constant 97% and 3%, respectively. The risk-free rate of return was 2%.
What are the M 2 measures for Miranda and the S&P 500? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
One-Year Trailing Returns Miranda Fund S&P 500 Return 10.2 % - 22.5 % Standard deviation 37 % 44 % Beta 1.10 1.00Explanation / Answer
M2 measure or Modigliani - Modigliani measure of investment return quantifies the risk adjusted return of an investment portfolio relative to a benchmark portfolio (the S&P 500 in this case)
Mirnada Portfolio Fund :
Return = R(p) =10.2%, Standard Deviation = SD (p) =37% and Beta = B(p) = 1.1
Weightage of Stock=97% and Weightage of Cash=3% ( with return equal to the risk free rate of 2%)
Therefore, return from stock = R(sp) =[R(p) - (0.03 x Risk Free Rate)] / 0.97 = 10.45%
Standard Deviation of Stocks = SD(sp) = SD(p) / 0.97 = (37/0.97) =38.14%
S&P 500:
Return = R(b) = 22.5%, Standard Deviation = SD(b) = 44%, Beta = B(b) =1
Weightage of Stocks = 97% (0.97) and Weightage of Cash = 3% (0.03) ( with risk free return of 2%)
Therefore, return from stock =R(sb) = [R(b) - (0.03 x 2)] / 0.97 = 23.13%
Standard Deviation of stocks = SD (sb) = SD(b) /0.97 = 44/0.97 = 45.36%
If the Miranda Fund now comprises of 50% stock and 50% cash, then
Returns from Miranda Fund = R(sp) x 0.5 + Risk Free Return x 0.5 = 10.45 x 0.5 + 2 x 0.5 = 6.225%
Standard Deviation of Miranda Fund = SD(sp) x 0.5 + Risk Free Return x 0.5 = 38.14 x 0.5 + 2 x 0.5 = 20.07%
Sharpe's Ratio of Miranda Fund = S1 = [Returns from Miranda Fund - Risk Free Rate] / SD of Miranda Fund
= [ 6.225 - 2] / 20.07 = 0.2105
Therefore, M2 Measure of Miranda Fund = S1 x SD(b) + Risk Free Rate = 0.2105 x 44 + 2 = 11.26
Similarly, Sharpe's Ratio of S&P 500 = S2 = (Returns from S&P 500 - Risk Free Rate) /SD of S&P 500= (22.5-2)/44 = 0.4659
Therefore, M2 Measure of S&P 500 = S2 x SD(b) + Risk Free Rate = 0.4659 x 44 + 2 = 22.5
NOTE: M2 Measure = Sharpe's Ratio of Portfolio (under consideration) x SD of Benchmark Portfolio + Risk Free Rate of Return. S&P 500 M2 measure is the same as the overall retun because this itself is the benchmark portfolio.
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