Question

• Table 2 shows regressions of the standard deviation and Sharpe ratio of household portfolio annual returns for different brackets of the distribution of net wealth in Sweden between 1999 and 2007 (standard errors are not reported). The reported Sharpe ratio of a household portfolio is equal to the expected return of the portfolio divided by its standard deviation. The Sharpe ratio is used to measure performance in relation to risk taken. For example, when comparing two portfolios, the one with the higher Sharpe ratio provides better return for the same level of risk. The Sharpe ratio is therefore a measure of the risk-adjusted return. What do the results indicate about portfolio diversification of households in Sweden? Explain your answer.

Table 2 Portfolio standard deviation and Sharpe ratio

Percentiles	Standard deviation	Sharpe ratio
50–55	0.137	0.401
55–60	0.143	0.403
60–65	0.149	0.405
65–70	0.156	0.408
70–75	0.164	0.411
75–80	0.171	0.415
80–85	0.179	0.420
85–90	0.188	0.425
90–95	0.200	0.432
95–97.5	0.212	0.441
97.5–99	0.221	0.448
99–99.9	0.236	0.449
100	0.262	0.432

Answer 1

Sharpe ratio describes how much excess return you receive for the extra volatility that you endure for holding a riskier asset. Remember, you always need to be properly compensated for the additional risk you take for not holding a risk-free asset.

S (x) = (r_x - R_f) / StdDev (x)

Where:

• X is the investment
• r_x is the average rate of return of X
• R_f is the best available rate of return of a risk-free security (i.e. T-bills)
• StdDev(x) is the standard deviation of r_x

The Sharpe ratio is a measure of return that is often used to compare the performance of investment managers by making an adjustment for risk.

Risk and reward must be evaluated together when considering investment choices; this is the focal point presented in Modern Portfolio Theory. In a common definition of risk, the standard deviation or variance takes rewards away from the investor. As such, the risk must always be addressed along with the reward when investment choices are to be made. The Sharpe ratio helps determine the investment choice that will deliver the highest returns while considering risk.

As per the above example,

the standard deviation,sharpe ratio and the risk premium(as per image) is increasing as per the increasing percentile of households.

This indicates that risk and rewards are in direct proportion.

It is but obvious that the risk premium followed by standard deviation and sharpe ratio is the greatest at 100 percentile and the least at 50 percentile