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October 27, 2009
How much leverage one can achieve depends on the prices of options, which in turn depend on the dividend yield and (more importantly) the volatility of the market. The long-term implied volatility of options on SPY is about 25% (see here) — considerably higher than the long-term average realized level of market volatility, which is around 15%-20%. The higher implied volatility raises prices for options and thereby reduces how many options you can buy with the 10% of the portfolio to be allocated to options. In the current market, you can buy 9.3 two-year at-the-money call options for the cost of one share of SPY. This is what provides the leverage. This leverage ratio will vary with time, but is easily calculated.
The simulated 90/10 portfolio has 90% in TIPS and 10% in the two-year at-the-money call options on SPY. Let’s look at the projected range of performance of this portfolio relative to the S&P500 and relative to TIPS.
Basic 90/10 Outcomes with 90% in TIPS and 10% in call options on SPY
The chart above shows the two-year projected cumulative returns for three portfolios:
- 100% invested in the S&P 500 (SPY)
- 100% invested in TIPS (TIP)
- 90% invested in TIP and 10% invested in the at-the-money call options (90/10)
The horizontal axis shows the probability that the portfolio will generate at or below the corresponding level of return found on the vertical axis. The vertical axis shows the cumulative return projected for a two-year period. At the far left of this chart, we can see the worst 2.5% of outcomes — the kind of extreme event that happens once in 40 years. For the S&P 500 (SPY), the Monte Carlo Simulation (MCS) estimates a cumulative two-year loss of -48% for the 2.5th percentile. This seems reasonable in light of recent years.
For TIPS, the MCS projects a worst case return over two years of -20%. Could this happen? It’s hard to say because TIPS were introduced relatively recently (1997 in the U.S.), but the MCS projected volatility for these bonds is higher than the implied volatility for these bonds: 11% in the MCS vs. 6.8% for options on TIP expiring in March 2010. There is no long-dated market in options on TIP. The trailing three-year realized volatility is 9.1%.
The 90/10 portfolio results (above) very nicely demonstrate the value of this strategy. In the worst case scenario (the far left), TIPS lose 20% and the call options expire worthless, so you have maximum losses on TIPS and the equity markets drop. The 1-in-40 worst case loses 28% — you have not lost maximum amounts on both the TIPS and the options because of their low correlation to one another.
This portfolio loses 28% over two years in its 1-in-40 worst case vs. a loss of 48% for the worst 1-in-40 case for the S&P500 over the two-year period. The 90/10 benefits from its big allocation to TIPS in a worst-case outcome. The S&P500 lost about 45% for the two years through February 2009, and TIPS returned a little more than 4% over this period. A 90/10 investor over this period would be down a little more than 6%, because the call options would expire worthless but the TIPS have appreciated slightly.
It is not until we look at the best outcomes that the strength of the 90/10 is clear. If the S&P500 has a huge rally, the MCS projects that the 95th percentile cumulative two-year return is 74%. The 95th percentile for the 90/10 portfolio is 73% for the two-year period because of the combined effects of both the TIPS having a great run and the call options becoming very valuable. The 90/10 has retained the potential to generate almost as much upside in great years as the S&P500, but it has a considerably tempered downside.
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