FIN 402 Week 5 Portfolio Management and Evaluation Example

Three Years In: Judging Rosa Delgado's Portfolio Against a Benchmark With the Sharpe Ratio, Treynor Measure and Jensen's Alpha, Then Writing the Policy That Will Manage It

[Student Name]

University of Phoenix

FIN/402: Investment Fundamentals and Portfolio Management

Week 5 Assignment

[Instructor Name]

[Date]

The investor, her returns and the benchmark figures are composites written for a model paper; the performance measures and research findings come from the sources listed.

Three years after investing her inheritance, Rosa Delgado's taxable account has grown from $85,000 to about $105,500, an average annual return of 7.4 percent after fees. She had followed the Week 3 plan, except that she put her U.S. stock allocation into an actively managed fund recommended by a friend rather than the index ETF. A colleague told her that 7.4 percent was a good result. Whether a return is good depends on what the same risk could have earned elsewhere, so the first task is to find the right comparison. This paper evaluates her portfolio and sets rules for managing it.

Choosing the Benchmark

A benchmark should hold the same kinds of assets in the same proportions as the portfolio, and an investor should be able to buy it cheaply. Rosa's account targets a half in domestic equities, roughly an eighth in foreign equities and the remaining 38 percent in bonds. The matching benchmark blends a U.S. total market index, an international index and a broad bond index in those weights. Over the three years it returned 7.9 percent a year with a standard deviation of 11.2 percent. Comparing her account with the S&P 500 alone, which returned 10.2 percent, would be unfair, because she deliberately took less risk.

Raw and Risk-Adjusted Returns

Rosa's portfolio returned 7.4 percent with a standard deviation of 11.8 percent and a beta of 0.68 relative to the U.S. stock market. Treasury bills averaged 3.5 percent. Her portfolio trailed the benchmark by half a point a year while being slightly more volatile.

The Sharpe ratio, introduced by Sharpe (1966), divides excess return by standard deviation. Her portfolio's ratio is 7.4 minus 3.5, or 3.9, divided by 11.8, about 0.33. The benchmark's is 4.4 divided by 11.2, about 0.39. She earned less reward per unit of total risk.

The Treynor measure divides excess return by beta. Her portfolio's is 3.9 divided by 0.68, about 5.7. It suits a portfolio held as part of a larger diversified plan, as Rosa's is alongside her 403(b).

Jensen's Alpha

Jensen (1968) measured a manager's contribution as the difference between the actual return and the return predicted by the capital asset pricing model. Plugging her 0.68 beta, the 3.5 percent bill average and the market's 10.2 percent into the model, the predicted return is 3.5 plus 0.68 times 6.7, or about 8.06 percent. Her actual return of 7.4 percent gives an alpha of about negative 0.66 percent a year. Because the portfolio holds bonds that the stock market beta does not fully capture, this alpha is approximate, but it agrees with the benchmark comparison.

Tracing the Shortfall

Breaking the results down by holding shows that the bond fund and the international fund matched their indexes after their low fees. The actively managed U.S. stock fund trailed its index by about 1.1 points a year, of which 0.82 points was its expense ratio. Weighted at 50 percent of the account, that fund explains nearly all of the half-point gap.

Will the Fund Recover?

Rosa's friend argued the fund would catch up. Carhart (1997) studied thousands of mutual funds and found that persistence in returns was largely explained by common factors and expenses, with little evidence of lasting skill, except that the worst performers tended to stay poor. Three years is too short to prove anything, but expenses are certain, and the research gives little reason to pay them in hope of a recovery.

How Much Does Half a Point Matter?

A shortfall of half a percentage point a year can look trivial. Over Rosa's remaining 21 years before retirement, it is not. At 6.9 percent a year, $105,500 grows to about $430,000; at 7.4 percent it grows to about $474,000. The gap of roughly $44,000 comes almost entirely from one fund's fees, money that would have stayed in her account with an index fund. Fees compound the same way returns do, which is why small annual differences matter so much over a long horizon. This calculation turned the evaluation from an abstract comparison of ratios into a decision Rosa could see clearly in dollars at retirement.

Costs Beyond the Expense Ratio

Expense ratios are not the only cost. Actively managed funds trade more, and trading costs and taxable distributions reduce returns further. Her active fund distributed capital gains in two of the three years, creating tax bills in her taxable account that an index ETF with low turnover would largely have avoided.

Drift and Rebalancing

Over three years, stronger stock returns pushed the account to 56 percent U.S. stocks, 13 percent international and 31 percent bonds, beyond the five-point band set in Week 3. Rebalancing restores the intended risk. Rosa can sell the active fund, which shows only a small gain, so the tax cost is low, buy the index ETF for 50 percent and add the remainder to bonds. Future contributions should go to whichever asset is below target, limiting sales and taxes.

The Investment Policy Statement

Return objective: grow the account at a rate that, with her 403(b), supports retirement at 65, assuming about 6.5 percent a year before inflation. Risk tolerance: moderate; she can accept a one-year loss of about 15 percent in the account without changing course. Time horizon: 21 years to retirement, then withdrawals over about 25 years. Liquidity: none needed from this account, since her emergency fund is separate. Taxes: favor broad index funds with low turnover in the taxable account and hold bonds in the 403(b) where possible. Target allocation: domestic stocks 50 percent, foreign stocks 12 percent and bonds 38 percent, each with a five-point band. Review: annually, comparing results with the blended benchmark on a risk-adjusted basis, and after any major change in her life.

Conclusion

Rosa's 7.4 percent return looks good in isolation but trails a fair benchmark on raw and risk-adjusted measures, and the shortfall traces to one fund's fees. Replacing it with an index fund, rebalancing to target and writing a policy statement turn the evaluation into a plan she can follow for the next two decades.

References

Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of Finance, 52(1), 57-82. https://doi.org/10.1111/j.1540-6261.1997.tb03808.x

Jensen, M. C. (1968). The performance of mutual funds in the period 1945-1964. The Journal of Finance, 23(2), 389-416. https://doi.org/10.1111/j.1540-6261.1968.tb00815.x

Sharpe, W. F. (1966). Mutual fund performance. The Journal of Business, 39(1), 119-138. https://doi.org/10.1086/294846