Question

CFA Question

James Chan is reviewing the performance of the global equity managers of the Jarvis University endowment fund. Williamson Capital is currently the endowment fund’s only large-capitalization global equity manager. Performance data for Williamson Capital are shown in Table 18.10.
TABLE 18.10 Williamson Capital performance data, 2007-2018

Average annual rate of return=22.1%
Beta=1.2%
Standard deviation of returns=16.8%

Chan also presents the endowment fund’s investment committee with performance information for Joyner Asset Management, which is another large-capitalization global equity manager. Performance data for Joyner Asset Management are shown in Table 18.11. Performance data for the relevant risk-free asset and market index are shown in Table 18.12.

TABLE 18.11 Joyner Asset Management performance data, 2007-2018
Average annual rate of return: 24.2%
Beta:0.8%
Standard deviation of returns:20.2%

TABLE 18.12 Risk-free asset and market index performance data, 2007-2018
Risk-Free Asset
Average annual rate of return: 5%

Market Index
Average annual rate of returns:18.9%
Standard deviation of returns: 13.8%
a) Calculate the Sharpe ratio and Treynor’s measure for both Williamson Capital and Joyner Asset Management.
b) The investment committee notices that using the Sharpe ratio versus Treynor’s measure produces different performance rankings of Williamson and Joyner. Explain why these criteria may result in different rankings.

Answer 1

a).

Williamson Capital:

Sharpe ratio is calculated as return of portfolio-risk free rate/standard deviation of portfolio= 22.1%-5%/16.8%= 1.02

Treynor ratio is calculated as return of portfolio-risk free rate/beta of portfolio= 22.1%-5%/1.2%= 14.25

Joyner Asset Management:

Sharpe ratio is calculated as return of portfolio-risk free rate/standard deviation of portfolio= 24.2%-5%/20.2%= 0.95

Treynor ratio is calculated as return of portfolio-risk free rate/beta of portfolio= 24.2%-5%/0.8%= 24

b).

Sharpe ratio and Treynor ratio are giving different performance rankings, as Sharpe ratio of williamson capital is highest and Treynor ratio of Joyner is highest.

The difference is because of the evaluation measure which both methods employ.

Sharpe ratio measures whether the portfolio is making significantly greater return for accepting the additional unit of risk associated with the portfolio.

whereas Treynor ratio measures how well a portfolio outperforms equity market as a whole by substituting beta for standard deviation in the sharpe ratio equation.