In a similar pattern to the last few weeks, we are moving away from simply Equity-based Mutual Funds to optimize, and exploring some more interesting areas of the market. Today, we will focus on the growing TIPS (Treasury Inflation Protected Securities) fixed income market, and the Fidelity Inflation-Protected Bond Fund.
Let’s begin with a basic explanation of what TIPS are. When you buy a Treasury bond, you are effectively buying two things, the par value of that bond and its accompanying coupon payment (exceptions are obviously discount instruments). The par value of the bond, for example, we will say $100.00, adjust in an inverse way to the prevailing interest rate of the market. The logic is that if you buy a Treasury bond for $100.00 at 5 percent, and interest rates then rise to 6 percent, people looking to buy bonds in the secondary market will not want your $100.00 bond at 5 percent when they can buy the same bond at 6 percent. Therefore your 5 percent bond will sell at a discount below $100.00. The inverse happens when interest rates fall below 5 percent and your 5 percent bond is now premium. TIPS protect you against inflation by adjusting the par value of your bond for whatever the inflation rate was on a semiannual basis. The interest rate is fixed, but applied to the adjusted par value, it rises with inflation and falls with deflation. However, even in the case of persistent inflation, the bond pays you the higher of the original principal or the inflation-adjusted principal at maturity. Due to some inherent complexity with these instruments, and the fact that the principal appreciation from inflation is taxed at regular income, Mutual Funds are preferred over buying TIPS outright.
The FINPX is a Fidelity TIPS Mutual Fund with an expense ratio of 0.45 percent and a minimum investment of $2,000.00. In the spirit of our article last week, let’s examine the return distribution to see which optimization method will be the most efficient.
The normal approximation above is actually not bad (to my surprise) but there are some worrisome incidences. First is the positive kurtosis, the data around the mean dwarfs the peak of the distribution. This is problematic, especially considering this is the population of returns and not just a sample, but not insurmountable. The more troublesome aspect here is the result of the positive kurtosis: the fat tails. The image below uses a t location distribution (the red line), which is designed to accommodate fatter tails, and it still misses a majority of the tail density.
Looking closely reveals that towards the opposing ends of the chart, there are small occurrences of extreme events. The reason for this is pretty clear. These are not things that happen in ‘normal’ market times. During the financial crises, all asset correlations broke down and equities, fixed income, etc. all fell in tandem. The idea is that unless we expect another financial crises to occur, we can somewhat discount these tail events. It is important to understand that diversification works under the assumption of asset correlations. If asset correlations break down, so does our diversification. There is no such thing as a perfect strategy. With that sobering fact in mind, let’s consider our optimization strategies.
This is an unusual case, and provides a fun opportunity. We are going to optimize according to traditional Mean-Variance, and Conditional Value at Risk proxies. Afterwards, we will compare and contrast the results.
The ETF’s that we are choosing to use were easy to select. All offer some sort of Inflation Protected Fixed Income strategy. Their expense ratios, as always, were lower than that of the Mutual Fund to guarantee a more inexpensive option. They are as follows.
- GTIP: iShares Global Inflation-Linked Bond ETF: .40 percent
- ITIP: iShares International Inflation-Linked Bond ETF: .40 percent
- LTPZ: 15+ Year U.S. TIPS Index Fund: .20 percent
- STIP: 0-5 Year TIPS Bond ETF: .20 percent
- STPZ: 1-5 Year U.S. TIPS Index Fund: .20 percent
- TDTF: iBoxx 5-Year Target Duration TIPS Index Fund: .20 percent
- TDTT: iBoxx 3-Year Target Duration TIPS Index Fund: .20 percent
- TIP: TIPS Bond ETF: .20 percent
- TIPZ: Broad U.S. TIPS Index Fund: .20 percent
- IPE: SPDR Barclays Capital TIPS ETF: .18 percent
- SCHP: U.S. TIPS ETF: .07 percent
We will first attempt the MV Optimization process.
This is an example that really shows the power of this process. We have three points highlighted on the graph. The first is the maximum risk/return trade-off on the efficient frontier, the second is the equally weighted portfolio of ETFs without optimization, and the third is the Mutual Fund being optimized. The Mutual Fund all the way at the bottom has roughly the same risk as the Maximum Sharpe Ratio portfolio, but doesn’t come close in the way of returns. The Mutual Fund achieves -160 basis points per unit of risk taken while the optimized portfolio achieves 650 basis points per unit of risk taken. We have listed these exceptional results below.
Portfolio with Maximum Risk/Return Tradeoff Weight
GTIP 48.85 percent
TDTF 51.15 percent
In addition to the boost in performance, this portfolio has no minimum investment requirements, and has a weighted expense ratio of .297 percent compared to .450 percent ratio for the FINPX.
Now that we have seen the far superior results of the MV Optimization technique, let’s take a look at the more robust CVaR Optimization. For a quick description of Conditional Value at Risk, see part I of my FFRHX optimization, but it basically adjusts for non-normal distributions. Since FINPX is not completely normal, the results of the CVaR Optimization would be applicable to investors that want to protect from extreme events, or believe that unusual market conditions will persist for the foreseeable future.
Above is the CVaR Optimization over a 1 month period. Since CVaR is slightly more sensitive, we optimize it over shorter periods. Towards the bottom of the figure, you can see the FINPX Mutual Fund. We can achieve lower CVaR along with significantly higher returns by optimizing the portfolio. Results here are also significantly better than the portfolio, but how do they compare with the MV Optimization? The risk is not comparable, however, the return and expense ratios are. While staying underneath the risk level of the Mutual Fund, we can achieve returns of up to 0.1 percent per month. Annualizing this gives us a yearly return of roughly 1.21 percent. At the point of risk for the Mutual Fund, we have a yearly return of 1.29 percent. So the MV Optimization process provides us with a slightly better risk/return tradeoff, but the increased robustness of the process could be more beneficial depending on the investor. Below is the optimum CVaR portfolio.
Portfolio with Maximum Risk/Return Tradeoff Weight
GTIP 55.57 percent
TDTF 44.43 percent
The two portfolios, you can see, are very similar. The difference is actually so slight that only an institution would really notice a difference. This bodes well for our assumption of normality in the MV optimization. The more this assumption is violated by the return distribution, the greater the difference between the results of the two methods.
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