SENIOR CITIZEN’S PENSION FUND paid no taxes on dividend income or on capital gains. The fund operated in a classical tax jurisdiction. The tax rate on dividends was somewhat higher than on realized capital gains. The fund was highly risk-averse, and the investment manager wanted to increase the fund’s excess return per unit of risk. This ratio is the Sharpe ratio. The numerator of the ratio is the difference between the expected annual return on the fund and the risk-free rate. The denominator is the standard deviation of the fund’s annual return.

Previously, the fund’s policy was to invest primarily for income, not capital gains. As the fund paid no tax, management thought it had an advantage in holding shares in companies that pay relatively high dividends. Shares that paid no dividends would be best left in the hands of high-tax payers. There were two problems with this strategy. First, it meant that the portfolio’s holdings were concentrated on mature companies with low-growth prospects. Second, this policy left the fund less diversified than was felt to be desirable.

In her preliminary analysis, the investment manager analyzed two hypothetical portfolios.

The first portfolio was similar to the existing portfolio, consisting of shares in companies with high-dividend-payout ratios. The second portfolio consisted of shares in companies that paid no dividends. Initially, she considered just three strategies:

(a) hold only the high-dividend portfolio;

(b) hold only the zero-dividend portfolio;

(c) invest half of the fund in each of the two portfolios.

The relevant data are the following:

The following formulas from Chapter 12 are relevant: 

Was the fund doing the right thing to focus its investment only on high-dividend-paying companies? What should the investment manager do?

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Expected return E(R) Standard deviation Correlation Sharpe ratio P1,2 Portfolio 1 0.12 0.20 0.3 0.25 Portfolio 2 0.10 0.22 0.3 0.19