MT483 Unit 4 Employer Stock Diversification Analysis Example

When the Paycheck and the Portfolio Share an Employer: An MT483 Unit 4 Diversification Analysis

[Student Name]

Purdue University Global

MT483: Investments

Unit 4 Diversification Analysis

[Instructor Name]

[Date]

Kevin Brooks, his employer and every volatility and correlation figure are composite; the sources cited are real.

The Position as Held

Kevin Brooks, a composite 34-year-old machinist, holds $85,000 in his employer's 401(k) plan: $51,000 in his employer's own stock and $34,000 in an S&P 500 index fund. That is 60 percent in one company, the same company that pays his wages. The analysis asks what diversification would do to the risk of this mix, and it uses three labeled assumptions. The employer stock's annual volatility is 34 percent, the index fund's 16 percent and an intermediate bond fund's 5.5 percent. The employer stock's correlation with the index fund is 0.55 and with the bond fund 0.10. These are composite inputs in the range typical of a mid-size industrial company, and the conclusions are tested against changes in correlation below.

Where Correlation Enters

Portfolio variance for Kevin's pair has three parts. The employer stock contributes its weight squared times its own variance; the index fund contributes the same for itself; and a cross term, where the two holdings interact, multiplies 2 by each weight, by 0.55 and by 34 and 16. The first two terms are each asset's own risk, scaled down by its weight. The cross term is where the assets interact. With a correlation of 1 it adds enough to make portfolio volatility equal the weighted average; with anything less, it adds less.

At Kevin's current mix the employer stock's part is 0.36 multiplied by 1,156, which is 416.16. The index fund's part is 0.16 multiplied by 256, which is 40.96. The cross term doubles 0.6 by 0.4 by 0.55 by 34 by 16 and comes to 143.62. Their sum is 600.74, and its square root is 24.51 percent. A simple weighted average of the two volatilities would be 26.8 percent, so the imperfect correlation already removes 2.3 points of risk.

The cross term is the only place where diversification happens, and it shrinks as correlation falls.

Two Partners, Stepped Down

Reducing the employer stock in steps of 20 points, and putting the difference into each partner in turn, gives the following volatilities.

1. 60 percent employer stock: 24.51 with the index fund, 20.74 with the bond fund.

2. 40 percent: 20.51 with the index fund, 14.31 with the bond fund.

3. 20 percent: 17.49 with the index fund, 8.46 with the bond fund.

4. 0 percent: 16.00 with the index fund, 5.50 with the bond fund.

The bond fund cuts risk faster at every step, for two reasons. Its own volatility is far lower, and its correlation with the employer stock is close to zero, so the cross term nearly disappears. The index fund partner helps less because it moves with the employer stock about half the time. Even so, moving from 60 to 20 percent employer stock with the index fund partner removes seven points of volatility, more than a quarter of the starting risk, without adding any bonds.

Correlation Alone, Moved

To isolate correlation, the panel holds a half-and-half mix of the employer stock and a 16 percent volatility partner and changes only the correlation between them. At 0.9 the portfolio's volatility is 24.45 percent; at 0.7 it is 23.31; at 0.5, 22.11; at 0.3, 20.85; and at 0.1, 19.50. Nothing about either asset changed except how they move together, yet risk fell by almost five points. Markowitz (1952) made this point the foundation of portfolio selection: the risk of a portfolio depends on the covariances among its holdings, not only on each holding's own risk. Correlations also change over time and often rise in sell-offs, so the low-correlation rows should be read as the more optimistic end of the range.

What a Bad Year Costs

Under a normal approximation, with an assumed mean return of 8 percent, a one-in-twenty bad year is 1.645 standard deviations below the mean. At Kevin's 24.51 percent volatility that is a return of about minus 32.3 percent, or a loss of about $27,471 on $85,000. At 20 percent employer stock with the index fund partner, the same calculation gives about minus 20.8 percent, or $17,655. Returns have fatter tails than the normal curve, so these figures understate the worst cases, but they translate volatility into a sum Kevin can picture.

Risk the Market Does Not Explain

With a correlation of 0.55, the share of the employer stock's variance that moves with the market is 0.55 squared, about 30 percent. The other 70 percent is specific to the company: its contracts, its managers, its competitors. That company-specific risk is the part diversification removes, and standard theory says it earns no extra expected return, because investors can shed it cheaply (Bodie et al., 2024).

Kevin's case adds a second exposure. His wages depend on the same company, so a bad year for the business could cut both his paycheck and his savings at once. Benartzi (2001) showed that plan members put more of their new contributions into their employer's shares when those shares had done well over the prior ten years, and that these heavier allocations did not predict how the shares performed afterward. The analysis does not tell Kevin what to sell; it shows that the 60 percent holding concentrates his risk in the one place where he is already most exposed.

References

Benartzi, S. (2001). Excessive extrapolation and the allocation of 401(k) accounts to company stock. The Journal of Finance, 56(5), 1747-1764. https://doi.org/10.1111/0022-1082.00388

Bodie, Z., Kane, A., & Marcus, A. J. (2024). Investments (13th ed.). McGraw Hill.

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