Question

A portfolio generates an annual return of 16%, a beta of 1.2, and a standard deviation of 19%. The market index return is 12% and has a standard deviation of 16%. What is the Sharpe measure of the portfolio and what is the Treynor measure of the portfolio if the risk-free rate is 6%? Explain the similarities and differences between the Sharpe ratio and Treynor measure. Also, explain the most appropriate application for each.

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Answer #1

Similarity between Sharpe ratio and Treynor ratio is that both measures tells us excess return per unit risk provided by portfolio

And the difference between both is that Sharpe measure use risk as standard deviation while Treynor measure use risk as beta .Standard deviation represent total risk while beta represents systematic or market risk .

Treynor measure is applied when we have well diversified portfolio because In case of well diversified portfolio,only Systematic risk is relevant While Sharpe measure is applied when portfolio is not well diversified and then total risk is required to be considered which is represented by standard deviation

Please use the following information on the portfolio and its
benchmark (S&P 500 index) to calculate
Portfolio
S&P 500
Average Annual Return
12%
10%
Standard Deviation
18%
15%
Beta
1.2
1
Risk-free rate =
2%
Sharpe ratio for the portfolio and S&P 500 index
Treynor ratio for the portfolio and S&P 500 index
Jensen’s alpha based on Capital Asset Pricing Model.

The expected return of stock A is 21% per year and the stock's
annual standard deviation is 46%. There is also a risk-free asset.
When a complete portfolio is formed with a portfolio weight on the
risky asset of 36%, the expected return on the complete portfolio
is 8.0%.
1. Compute the risk-free rate of return.
2. Compute the annual standard deviation of the complete
portfolio above.
3. Compute the market price of risk using the Sharpe ratio?

The following table provides information about the portfolio
performance of three investment managers: Manager Return Standard
Deviation Beta A 25% 22% 2.1 B 21% 19% 1.5 C 15% 10% 0.8 Market (M)
15% 12% Risk Free Rate = 5% Complete the following table: Manager
Expected Return Sharpe Ratio Treynor Ratio Jensen’s Alpha A B C
Rank

The following table provides information about the portfolio
performance of three investment managers:
Manager
Return
Standard Deviation
Beta
A
25%
22%
2.1
B
21%
19%
1.5
C
15%
10%
0.8
Market (M)
15%
12%
Risk Free Rate = 5%
Complete the following table:
Manager
Expected Return
Sharpe Ratio
Treynor Ratio
Jensen’s Alpha
A
B
C
Rank

The following table provides information about the portfolio
performance of three investment managers:
Manager
Return
Standard Deviation
Beta
A
25%
22%
2.1
B
21%
19%
1.5
C
15%
10%
0.8
Market (M)
15%
12%
Risk Free Rate = 5%
Complete the following table:
Manager
Expected Return
Sharpe Ratio
Treynor Ratio
Jensen’s Alpha
A
B
C
Rank

If the return on portfolio A is 10%, the market portfolio return
is 12%, the inflation rate is 2%, the risk-free rate is 3%, the
standard deviation of the return for portfolio A is 8% and the
standard deviation of the return on the market portfolio is 14% and
the beta of portfolio A is 0.6, the Treynor ratio for portfolio A
will be 0.083.
A. True
B. False

Suppose the risk-free return is 4%. The beta of a managed
portfolio is 1.2, the alpha is 1%, and the average return is 14%.
Based on Jensen's measure of portfolio performance, you would
calculate the return on the market portfolio as

The stock of a Company has a beta of 1.2 has a standard
deviation of returns of 25%. The market portfolio is expected to
return 12% and the risk-free rate is 2%. If the market portfolio
has a standard deviation of 15%, how much of the risk of XYZ stock
is market risk and how much is non-market risk?

Last year your portfolio of small cap stocks produced a return
of 32%. The S&P 500 had a return of 26% for the same period.
Your portfolio had a beta of 2 and a standard deviation of 34%. The
S&P had a standard deviation of 22% and the risk free rate was
8.0%.
Calculate the Sharpe Ratio, Treynor
Ratio, and Jensen’s Alpha for your portfolio.
Discuss (in depth/be thorough) how your portfolio
performed last year.

1.2. The risk-free rate is 6%, the expected return on the market
portfolio is 14%, and the standard deviation of the return on the
market portfolio is 25%. Consider a portfolio with expected return
of 16% and assume that it is on the efficient frontier.
1.2.1. Calculate the beta of this portfolio (4).
1.2.2. Calculate the standard deviation of its return (5).

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