As discussed in the article on asset allocation, our investment method picks the mix of TSP funds that maximizes expected returns while not exceeding a fixed maximum risk. This leads to a natural question — What exactly is risk? When it comes to investments, many people have an intuitive understanding of what risk is. For instance, if an investment strategy performs well in a market crash, then, intuitively, it has a relatively low risk. However, to calculate the optimal asset mix, we need to have a precise mathematical definition of risk. Several such definitions exist, including the the standard deviation of logarithmic return, used in modern portfolio theory, and target semi-deviation of logarithmic return, used in post-modern portfolio theory. We use a proprietary mathematical definition of risk that is different from these. We feel that our definition is better on theoretical grounds. The past performance of our investment strategy appears to confirm this.
Though risk is often discussed in the financial media, few people know its actual mathematical definition. Intuitively, many of us understand what risk is. When the price of an investment is moving relatively smoothly, the risk of the investment is low; when the price is jumping up and down, all over the place, the risk is high.
An intuitive approach to assessing risk is to consider what happens to an investment strategy during stock market crashes. As we learned in the 1990's, it's easy to make money in stocks when the stock market as a whole is booming. One could just pick a random collection of stocks and still make money. In the words of Burton Malkiel, an economics professor at Princeton, "a blindfolded monkey throwing darts at a newspaper's financial pages" could do well in those times.[1]
It's not that picking random stocks is not risky. Picking random stocks is very risky. But when the market as a whole is booming, this risk is masked by the overall upward trend. The risk of an investment strategy becomes more apparent when the market is in a decline. That's why considering what happens to a strategy in a market decline is a good intuitive measure of its risk. For example, if an investment strategy has lost 5% while at the same time the stock market, as measured by some index, has lost 40%, then clearly the strategy is much less risky than stocks.
While this is a great intuitive meaure of risk, its limitation is that each market crash in essence becomes just one data point. For accurate decision-making, more rigorous measures of risk are needed.
A popular mathematical definition of risk is the standard deviation of logarithmic return.[2] This definition, also called "volatility", is used in a financial model called modern portfolio theory. One criticism of this risk measure is that it penalizes both positive and negative deviations from the mean equally. That is, an unusually high return increases this risk measure by the same amount as an unusually low return. However, from an intuitive point of view, there is nothing risky about a return that is "too high". Thus, this risk measure somewhat captures what people mean when they use the word "risk", though not exactly.
There is another financial model, called the post-modern portfolio theory. It is called this because it builds on the modern portfolio theory. In post-modern portfolio theory, risk is mathematically defined as the target semi-deviation of logarithmic return.[3] That is, returns that are "too high" do not influence the risk measure. Risk, in this model, is only influenced by returns that are "too low" relative to some target. This risk measure is certainly an improvement on the simple standard deviation that is used so often. However, it does have its own issues.
In the asset allocation method that we use to allocate money among TSP funds, we use a precise mathematical definition of risk. This proprietary definition was developed by our founder, a Ph.D. statistician. In our opinion, the definition is better than others that we have seen on theoretical grounds. From a practical point of view, we see based on past returns that it has worked well. Both our Conservative and our Balanced allocations have higher long-term returns than any of the TSP funds. The Lifecycle funds themselves employ an asset allocation approach, though it is different from ours. Following market portfolio theory, they define risk as volatility. Our allocations outperform all of the Lifecycle funds as well.
| Long-term annual return* | |
|---|---|
| Peaceful Gains | |
| Conservative | 8.97% |
| Balanced | 13.66% |
| Year-to-date** | |
|---|---|
| Peaceful Gains | |
| Conservative | 0.61% |
| Balanced | -0.20% |
| TSP Individual | |
| G Fund | 0.85% |
| F Fund | 0.49% |
| C Fund | -1.88% |
| S Fund | 2.97% |
| I Fund | -4.21% |
| TSP Lifecycle | |
| L Income | 0.73% |
| L 2010 | 0.44% |
| L 2020 | -0.09% |
| L 2030 | -0.34% |
| L 2040 | -0.68% |
* Compound annual growth rate, 1995-2008.
** Ending May 1, 2009.
Starting October 15, 2008, returns for our allocations are verified by a third party. Returns prior to that are simulated.