MT422 Unit 10 Portfolio Construction Proposal Example

What Each Holding Adds to Risk: An MT422 Unit 10 Portfolio Construction Proposal for an Air Traffic Controller

[Student Name]

Purdue University Global

MT422: Portfolio Management

Unit 10 Portfolio Construction Proposal

[Instructor Name]

[Date]

The investor, her accounts and every return, risk and correlation figure are composite assumptions supplied for the exercise; fund types are described as structures, not named products, and the sources cited are real.

The Investor

Marisa Okafor, a composite 44-year-old, works as an air traffic controller at an en route center near Kansas City. Most controllers face mandatory separation at 56, so her horizon to retirement is about twelve years, followed by a decade or more of withdrawals before Social Security begins at full value. Her workplace savings sit in the Thrift Savings Plan in a target-date fund, reviewed separately. This proposal covers a $238,000 taxable brokerage account built from the sale of a rental house. She wants broad funds rather than single stocks, can tolerate a bad year if she understands it in advance, and wants protection against inflation eroding her savings before her pension and Social Security begin.

The Proposed Holdings

The proposal holds 34 percent in a U.S. large-company index fund, 8 percent in a small-company value fund, 16 percent in a developed international index fund, 6 percent in an emerging markets index fund, 26 percent in an intermediate-term bond index fund and 10 percent in a Treasury inflation-protected securities fund. Stocks total 64 percent and bonds 36 percent.

Supplied Assumptions

Expected returns and standard deviations are assumed as follows: U.S. large companies 7.0 and 16.0 percent, small value 8.0 and 21.0, developed international 7.0 and 17.0, emerging markets 8.0 and 23.0, intermediate bonds 4.3 and 5.5, and inflation-protected Treasuries 4.0 and 6.0. Stock funds are correlated with each other between 0.65 and 0.85, bonds with stocks at about 0.10, inflation-protected Treasuries with stocks at about 0.15, and the two bond funds with each other at 0.75. These are assumptions for the exercise, not forecasts.

The Portfolio as a Whole

Using the full covariance matrix, the portfolio's expected return is 6.14 percent and its standard deviation 10.76 percent. Markowitz (1952) showed that this figure, not the deviation of any single holding, is what the investor actually bears, because holdings that move differently offset some of each other's swings.

In dollars, a 6.14 percent year adds about $14,600 to the account. A bad year, one that the assumptions suggest should occur about once in twenty, would be about 11.6 percent below zero, a loss of roughly $27,500. Marisa said a loss of that size would be uncomfortable but not a reason to sell, which is the test the allocation needs to pass.

Where the Risk Comes From

Each holding's contribution to portfolio variance equals its weight times its covariance with the whole portfolio, divided by the portfolio's variance. The contributions sum to 100 percent.

The U.S. large-company fund contributes 48.1 percent of the risk with 34 percent of the money. Developed international contributes 22.5 percent with 16 percent of the money. Small value contributes 13.6 percent with 8 percent, and emerging markets 10.3 percent with 6 percent. The intermediate bond fund contributes 3.7 percent of the risk with 26 percent of the money, and inflation-protected Treasuries 1.7 percent with 10 percent.

Stocks are 64 percent of the money and about 95 percent of the risk; the bonds hold their place by not adding to it.

Capital weights therefore understate how much the portfolio depends on stocks. Maillard et al. (2010) describe portfolios built to equalize these risk contributions; this proposal does not aim for equal contributions, but measuring them shows that any decision about the stock mix is, in effect, a decision about nearly all of the portfolio's risk.

Why Each Holding Is There

The U.S. large-company fund is the core: the broadest, cheapest exposure to the market in which Marisa will spend her retirement income. Developed international adds companies whose returns depend on other economies and currencies, which lowers risk slightly relative to holding the same stock weight in U.S. companies alone. Small value adds exposure to smaller and cheaper companies, which have historically earned higher returns than large companies over long periods, though with long stretches of underperformance; at 8 percent it is large enough to matter and small enough not to dominate. Emerging markets add growth from economies outside the developed world at the highest volatility in the portfolio, which is why it is held at only 6 percent.

The intermediate bond fund steadies the portfolio and provides money to rebalance from after a stock decline. Inflation-protected Treasuries address Marisa's stated worry directly: their principal rises with consumer prices, protecting the purchasing power of savings she will need in the years between leaving work and full Social Security.

Costs

Weighted by the holdings, the expense ratios average 0.062 percent, about $148 a year on $238,000. The small-value fund, at 0.25 percent, is the most expensive holding and accounts for about a third of the total cost with 8 percent of the money; its place depends on whether its expected premium justifies that cost, and the proposal judges that it does at this weight.

Testing a Simpler Alternative

A three-fund mix of 50 percent U.S. stocks, 20 percent developed international and 30 percent bonds is a common and reasonable alternative. Under the same assumptions it returns 6.19 percent at a deviation of 11.21 percent, with costs of 0.040 percent, about $95 a year. Its return per unit of risk above a 4 percent bill rate is 0.195, against 0.199 for the proposal.

The two portfolios are close. The proposal's extra holdings lower risk a little and cost about $53 a year more. The case for them rests less on the small improvement in return per unit of risk than on the inflation protection Marisa asked for, which the three-fund mix does not provide. Brinson et al. (1986) traced most of the quarter-to-quarter swings in large pension plans' returns to their policy mix of stocks, bonds and cash rather than to security selection or timing, which is a reminder that the stock and bond split matters far more than the choice between these two versions of it.

Coordinating With Her Other Savings

Bond income is taxed at ordinary rates each year, so bonds are usually more tax-efficient inside a tax-deferred account. If Marisa's Thrift Savings Plan can hold more of her overall bond exposure, through its government securities or fixed income funds, this taxable account could hold a higher share of stocks while her overall allocation stays the same. That change should be made only when both accounts are reviewed together.

Rebalancing and Review

Once a year the six weights are reset to target, and an earlier reset happens whenever one holding wanders five points or more away from its own. New contributions go to whichever holding is furthest below target. The allocation is reviewed at age 50 and again at 54, with the bond share rising as retirement approaches.

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

Maillard, S., Roncalli, T., & Teiletche, J. (2010). The properties of equally weighted risk contribution portfolios. Journal of Portfolio Management, 36(4), 60-70. https://doi.org/10.3905/jpm.2010.36.4.060

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