Question
In: Finance
The following table repeats the annual total returns on the MSCI Germany Index previously given and...
The following table repeats the annual total returns on the MSCI Germany Index previously given and also gives the annual total returns on the JP Morgan Germany five- to seven-year government bond index (JPM 5–7 Year GBI, for short). During the period given in the table, the International Monetary Fund Germany Money Market Index (IMF Germany MMI, for short) had a mean annual total return of 4.33 percent. Use that information and the information in the table to answer the following questions.
| Year | MSCI Germany Index (%) | JPM Germany 5-7 Year GBI (%) |
| 1993 | 46.21 | 15.74 |
| 1994 | -6.81 | -3.40 |
| 1995 | 8.04 | 18.30 |
| 1996 | 22.87 | 8.35 |
| 1997 | 45.90 | 6.65 |
| 1998 | 20.32 | 12.45 |
| 1999 | 41.20 | -2.19 |
| 2000 | -9.53 | 7.44 |
| 2001 | -17.75 | 5.55 |
| 2002 | -43.06 | 10.27 |
a) Using the IMF Germany MMI as a proxy for the risk-free return, calculate the Sharpe ratio for:
(i) the 60/40 equity/bond portfolio described in Problem 12.
(ii) the MSCI Germany Index.
(iii) the JPM Germany 5–7 Year GBI.
b) Contrast the risk-adjusted performance of the 60/40 equity/bond portfolio, the MSCI Germany Index, and the JPM Germany 5–7 Year GBI, as measured by the Sharpe ratio.
Solutions
Expert Solution
a.) Sharpe ratio for the MSCI Germany Index.
Sharpe Ratio = (Rx – Rf) / StdDev Rx
Where:
- Rx = Expected portfolio return
- Rf = Risk free rate of return
- StdDev Rx = Standard deviation of portfolio return / volatility
| Column1 | Year | MSCI Germany Index (%) | JPM Germany 5-7 Year GBI (%) |
| 1993 | 46.21 | 15.74 | |
| 1994 | -6.81 | -3.4 | |
| 1995 | 8.04 | 18.3 | |
| 1996 | 22.87 | 8.35 | |
| 1997 | 45.9 | 6.65 | |
| 1998 | 20.32 | 12.45 | |
| 1999 | 41.2 | -2.19 | |
| 2000 | -9.53 | 7.44 | |
| 2001 | -17.75 | 5.55 | |
| 2002 | -43.06 | 10.27 | |
| Return | 10.74 | 7.92 | |
| StdDev | 29.99 | 6.94 |
Sharpe Ratio = (10.74 - 4.33)/29.99
Sharpe Ratio = 0.21
ii.) the JPM Germany 5–7 Year GBI.
Sharpe Ratio = (7.92 - 4.33)/6.94
Sharpe Ratio = 0.52
b.) The Sharpe ratio of the JPM Germany 5–7 Year GBI is higher than that of the MSCI Germany Index. As a result, the JPM Germany 5–7 Year GBI index returns are more relative to the amount of investment risk it has taken. Hence, as per risk adjusted performance it is better to invest in JPM Germany 5–7 Year GBI.
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