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Wrong Objective

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Optimizing for the Wrong Objective

To understand the importance of these different approaches, we need to understanding a little something of how investment models are built. The basic idea is to find the optimal portfolio to maximize risk adjusted returns, or returns relative to their risk level. This makes people feel comfortable with the daily fluctuations in their net worth and then they are free to maximize wealth in that context. When their risk level is too high, they might be inclined to use less risky assets such as Treasury Bills (TB) to create their optimal portfolio. TB returns are lower than the returns for TIPs, but the risk is lower as well, justifying the purchase. But if their real goal is to protect their income, cash is actually very risky and lower in returns than TIPs, which are risk free. Also, using wealth maximization without considering the relationship to our income needs can lead to strategies that work over the long run on average but fail miserably when you look at the annual contours of the decisions we need to make.

Let’s take very simple example. While we don’t have access to the same data as Professor Merton, we will take monthly returns from 2003-2012 for TB, 10 year Treasury Notes (10TN - constructed returns), 10 year TIPs (TIPs - constructed returns), the Wilshire 5000 for stocks and MSCI EAFA for international stocks. Please note for illustration purposes, we reduced the TB returns by 25% because they were unusually high for this period relative to bonds. We are also going to assume that 10 year TIPs are the perfect hedge against our future liabilities for life, although the one chosen by Professor Merton was more appropriate. We are trying to inspect how the decision process works, not produce an optimal portfolio so this is only an illustration.

Below we calculate the returns and risk levels for each asset class. However, the risk level for each class is calculated in two different ways. First is the standard deviation (SD) of returns above TB (or excess returns over the riskless asset) and second is the SD of returns less TIPs, which is considered the riskless asset from the income protection standpoint:

10 TN

3 Mo TB

10 TIPs





















Note the SD of TB is 0.35% normally, but 7.6% when used for income protection. The TIPs price risk is 7.63%, but zero for income protection. So if we are going to create an optimal portfolio for wealth maximization, TB are attractive for risk reduction purposes, but not for income. If we focus on income protection, TB is not attractive for any reason, but TIPs are for risk reduction purposes. Also, the returns for 10TN are about the same as for TIPs with similar risk levels for wealth maximization. But there is an enormous difference in risk level for income protection. Let’s see what happens.

We ran a simple optimization using an iterative process to produce for a set risk level, both SD TB and SD TIPs. The allocation produced the following results:

Wealth Max Income Protect Wealth Max Income Protect
3 Mo TB 17% 0% Return 5.34% 5.63%
10 TIPs 12% 42% SD 5.25% 6.78%
10 TN 44% 25% SD Excess 5.27% 5.27%
Wilshire 27% 16% SD TIPs 5.52% 5.27%
EAFA 1% 18%

First we note the overall risk (SD TIPs) and return level for the wealth approach produces lower returns and higher risk when measured from the income protection standpoint. This fact is not surprising as the program optimized for the wrong objective. Also, while the return is higher for income protection, the total SD is also higher. This is not surprising because the income protection program measures TIPs as zero risk when the market price volatility is higher. Again, the market risk represents opportunity cost as discussed above and should be monitored but not considered the most important factor. The SD Excess is the risk factor of each relative to their objective: TB for wealth maximization and TIPs for income protection. The program solved to equalize these risks to draw a fair comparison.

Note the program picked up TB when maximizing wealth for 17% of the portfolio, but dropped it when seeking to protect an income level because it is a low return/high risk asset. There was also a substantial reduction in 10 TN in favor of TIPs because the risk was lower and returns were similar. Some of the reduction in TB increased equities. So the actual risk reduction from TIPs, an asset that produces a bond like return itself, freed the portfolio up to invest more in stocks without increasing the overall income protection risk. In this case it would seem to defy common sense to invest in TB or favor TN over TIPs when income protection is our real objective, yet when we use wealth maximization techniques that is precisely what we do. Lastly we should note that the moderate risk wealth maximization portfolio invested 88% of their assets without any protection from inflation, which is the primary threat to income protection. A moderate risk portfolio for income protection had 58%. This decisions also seems to defy common sense.

Next Article in series: Real World

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