Question

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.

Answer 1

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.