FIN 402 Week 3 Diversification and Asset Allocation Example

Sixty, Forty or Something Else? Building Rosa Delgado's Asset Allocation From Correlation, Portfolio Risk, Time Horizon and Her Response to a Bad Year

[Student Name]

University of Phoenix

FIN/402: Investment Fundamentals and Portfolio Management

Week 3 Assignment

[Instructor Name]

[Date]

The investor, her fund assumptions and the allocation are composites written for a model paper; portfolio theory and research findings come from the sources listed.

Rosa Delgado, the composite respiratory therapist, now holds her inheritance in a stock index ETF and a bond fund, and she contributes 8 percent of her pay to the hospital's 403(b) plan, which holds a target-date fund. She plans to retire in 24 years. After Week 2 showed her that the stock fund could lose 14 percent in a recession, she asked how much she should hold in each. Asset allocation is the decision that sets most of the risk an investor will live with, so it deserves more care than the choice of any single fund. This paper builds her allocation.

Why Diversification Works

Markowitz (1952) showed that an investor should judge a security by its effect on the whole portfolio, not on its own. A portfolio's variability depends on the variability of each holding and on how the holdings move together. When returns are less than perfectly correlated, losses in one asset are partly offset by gains or smaller losses in another, so the portfolio varies less than the weighted average of its parts. That reduction is the only benefit in investing that costs nothing.

Two Kinds of Risk

Diversification removes unsystematic risk, the part of a stock's swings caused by events at one company, such as a failed product or a lawsuit. It cannot remove systematic risk, the swings that affect nearly all stocks, such as recessions and changes in interest rates. Statman (1987) estimated that a randomly chosen portfolio needed at least 30 stocks for most of the benefit of diversification, and later researchers argued that more are needed today as individual stocks have become more volatile. Rosa's index ETF holds 500, so her stock risk is almost entirely systematic.

The 60/40 Calculation

For planning, the analysis assumes the stock fund has an expected return of 8 percent and a standard deviation of 18 percent, the bond fund 4.5 percent and 6 percent, and a correlation between them of 0.1. A 60 percent stock and 40 percent bond portfolio has an expected return of 0.6 times 8 plus 0.4 times 4.5, or 6.6 percent. Its variance is 0.36 times 324, plus 0.16 times 36, plus two times 0.6 times 0.4 times 18 times 6 times 0.1, which sums to 116.6 plus 5.8 plus 5.2, or about 127.6. The standard deviation is the square root, about 11.3 percent.

Averaging 18 and 6 by the same 60 and 40 weights would suggest 13.2 percent. Because the assets are only weakly correlated, the portfolio's risk is almost two points lower. If the correlation were 1, there would be no reduction; if it were negative, the reduction would be larger.

Adding International Stocks

An international stock fund with an expected return of 8 percent, a standard deviation of 19 percent and a correlation of about 0.75 with U.S. stocks adds a smaller benefit, since it moves more closely with Rosa's existing stocks. Replacing a sixth of her U.S. stock allocation with international stocks lowers the stock portion's standard deviation slightly and reduces dependence on one economy. Correlations among stock markets tend to rise in crises, so the benefit is modest when it is needed most.

The Weight of the Allocation Decision

Brinson et al. (1986) studied 91 large pension plans and concluded that the policy mix each plan held over time accounted for an average of 93.6 percent of the variation in the plans' quarterly returns over time, with security selection and timing explaining little. The study measures variation, not the level of return, but the lesson for Rosa is the same: her stock and bond split will drive her experience far more than which stock fund she picks.

Testing the Mix Against a Bad Year

Numbers on paper become real in a downturn, so the analysis tests the recommended mix against a severe year. In 2008, a broad U.S. stock index lost roughly 37 percent while high-quality bonds gained about 5 percent. A 60/40 portfolio with those returns would have lost about 20 percent, or $17,000 on Rosa's $85,000, compared with more than $31,000 for an all-stock account. An 80/20 mix would have lost about 29 percent. Showing Rosa these dollar figures, rather than standard deviations, gave her a clearer sense of what each choice would feel like. She said a loss near $17,000 would be painful but survivable, while a loss above $25,000 might push her to sell. That answer narrowed the choice more than any questionnaire.

Her Tolerance for Losses

Rosa's horizon of 24 years gives her capacity to hold mostly stocks, since she has time to recover from downturns. Her willingness is lower: a questionnaire placed her as moderate, and she admitted she would have been tempted to sell during the 2020 market drop. An allocation she would abandon in a crash is worse than a more conservative one she would keep. Her capacity and her willingness point to a middle ground.

Looking at the Whole Household

Her 403(b) target-date fund is about 85 percent stocks. With $62,000 there and $85,000 in the inheritance account, a 60/40 split in the inheritance account would make her total allocation roughly 71 percent stocks. That is reasonable for her age and tolerance. It also suggests holding the bonds in the 403(b), where interest is tax-deferred, if the plan's options allow, while keeping stock index funds in the taxable account.

Recommendation

Rosa should target about 70 percent stocks and 30 percent bonds across both accounts, with a fifth of the stocks in an international fund. In the inheritance account, that means about 50 percent U.S. stocks, 12 percent international stocks and 38 percent bonds. She should rebalance once a year, or sooner if stocks drift more than five points from target, adding new money to the lagging asset before selling anything.

Conclusion

Diversification lowers Rosa's risk because her assets do not move in step, and the arithmetic shows a 60/40 portfolio carrying less risk than its parts. Her long horizon supports a stock-heavy mix, her caution argues against the most aggressive choice and her retirement plan changes the household total. A 70/30 allocation with an annual rebalancing rule fits all three.

References

Brinson, G. P., Hood, L. R., & Beebower, G. L. (1986). Determinants of portfolio performance. Financial Analysts Journal, 42(4), 39-44. https://doi.org/10.2469/faj.v42.n4.39

Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x

Statman, M. (1987). How many stocks make a diversified portfolio? Journal of Financial and Quantitative Analysis, 22(3), 353-363. https://doi.org/10.2307/2330969