Question

An actively managed portfolio on Canadian energy stocks has achieved a 32% return this past year with a volatility of 48%. By comparison, the portfolio’s benchmark, the S&P/TSX Energy Index returned 22% with a volatility of 35%. The risk-free rate during this time was 1%.

1. Calculate the Sharpe Ratio of both portfolios. Which offered the best risk-adjusted return?
2. What was the Jensen’s alpha of the actively managed portfolio, relative to its benchmark, assuming the correlation between the managed portfolio and the benchmark was 0.79?
3. Assuming the same correlation as in part b, what was the actively managed portfolio’s M²?
4. What is the Treynor Ratio for both the actively managed portfolio and its benchmark?
5. Assuming normally distributed returns and a single-index model with the benchmark as the single factor, calculate the information ratio of the active portfolio

Answer 1

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Answer:

a)

Sharpe Ratio (SR) is given by the formula as Asset A return-Rf/standard deviation

• Actively managed portfolio Sharpe Ratio = 32%-1% / 48% = 0.6458
• Benchmark (S&P/TSX) Sharpe Ratio = 22%-1% / 35% = 0.6

Actively managed portfolio is the better one asoffered the best risk-adjusted return. (Higher sharpe ratio).

b)

Jensens's Alpha is the formula as R(i) - (R(f) + B x (R(m) - R(f)))

Beta = 0.79* (48%/35%) = 1.0834

Jensen alpha for actively managed portfolio =>32% - ( 1%+ (1.0834* (22%-1%)))= 32%-23.75% = 8.2486 %.

c)

M2 can be computed as Sharpe Ratio *Standard deviation of benchmark+ risk-free rate

M2 = 0.6458*35%+1% = 0.232488 = 23%

d)

TR = Ra-Rf/Beta

TR of actively managed portfolio = 32%-1%/1.0834 = 0.2861 = 28.61%

TR of benchmark = 22%-1%/1 =21%

e)

Information ratio = Ri - R(b)/SD or active

= 32% - 22%/0.48 = 0.2083