Thursday, May 22, 2008

In-Depth Performance Analysis

My main task this month is the annual rebalance of the asset allocation portfolio. It’s quite a hassle, involving the re-jigging of literally half a dozen accounts. Prior to that however, I've decided to take a deeper look at my performance to-date and see if the allocation plan itself needs changing (see current allocation here). The last time I took such an in-depth look was the end of 2006 when I had much less data.

Each month I calculate percent gains or losses for my AM, AA and total portfolios, as well as that of the benchmark index ETFs that are dividend-adjusted. So far I have data from 1/11/2006 to 5/5/2008. I have been fairly consistent in my approach, but there are a few aberrations. Jan 2006 was a partial month since this blog wasn’t launched till the 11th, as a result, my performance was shortchanged by about 4% relative to the S&P (Commodities and emerging markets were going gangbusters then). I missed the end of last month by a couple of days due to my vacation. In between, I also missed November and December of last year due to my computer woes, so the October entry last year actually encompassed the entire 4th quarter. While the data series wasn’t perfect, I made sure that the benchmark ETFs and my portfolios were calculated the same way so that a meaningful comparison can still be made.

The two charts above give a graphic representation of my returns versus the dividend-adjusted SPY. I choose SPY becaus the S&P 500 appears to be the most popular benchmark for money managers. At any rate, VTI (Wilshire 5000 index ETF), which is probably a better benchmark for my investing style, was very similar during this period. The first chart shows the monthly gains in a bar graph. It's evident that my portfolios, especially the AM portfolio, are quite volatile. The max monthly gain was almost 12% and the max loss about -8%. The second chart shows the cumulative performance which is really where the meat, or rather the dough, is. Here my portfolios handily beat SPY with most of the gain came from the AM portion. After 28 months, the AM portfolio gained 40% or 15.5% annualized. The AA portfolio gained 16.5% or 6.8% annualized. The total portfolio returned 29%, 11.5% annualized, while SPY returned 13.4% or 5.6% annualized.

Next I plot the monthly gains vs. SPY as well as the linear regressions. This is the classical treatment from Markowitz’s Capital Asset Pricing Model (CAMP). The slope of the line is the "beta", a measure of portfolio risk; and the intercept "alpha", a measure of manager's skill. The AA portfolio has (relatively) the best fit as shown by the (still small) R2 value of 0.55. The intercept of 0.004 indicates that the AA portfolio is beating SPY by an average of 0.4% per month; however, the R2 says there's a 45% chance that such outperformance was due to luck. The "beta" of the AA portfolio was 0.6. In other words, it was deemed to be taking only 60% of the market risk. due to the poor fit, one shouldn't put much store in that number. The other lines had such low R2 numbers that they don't warrant much comment other than that the larger alphas were consistent with the larger gains. My AA portfolio had sizable deviations from SPY due to the presence of PM and commodities (16%), alternative assets (15%) and fixed income (20%). The correlation between the AM portfolio and SPY was non-existent due to heavier presence of PM and commodities, and the use of shorting and market timing.

The Sharpe ratio (SR) is a more meaningful measure of portfolio performance. It's also called risk-adjusted-return, defined as

SR = (R – Rf)/StdDev(R)

Where R is the average return; Rf is the risk-free rate; and StdDev(R) is the standard deviation of R. The numerator is the actual return above the risk-free rate, also called the excess return. The denominator is the standard deviation of the return, the technical measure of volatility. The SR, therefore, gives the return per unit of risk. There is a nice collection of web-based calculators including detailed instructions for this calculation at Bill Sharpe's website.

I calculated SR twice, once with a risk-free rate of 0 and once with a constant rate of 3%. Sharpe's calculator uses the rate of Vanguard's short-term treasury fund as the risk-free rate. It's more exact but I couldn't be bothered. In general, increasing the risk-free rate in the above equation favors the high-risk, high-reward approach.

The standard deviation of returns describe how volatile the investment is. My AA portfolio is about 80% as volatile as SPY and VTI in this sense. My AM portfolio is quite volatile, second only to EEM. The combined total is about equivalent to IWM, i.e. a portfolio full of small cap stocks. My SRs are quite respectable, beaten only by EEM, which although very volatile, also had the most gain. Note that the SR of the total portfolio is greater the AM and AA portfolios separately -- a vindication of my overall strategy.

I started this exercise to see if my allocation plan needs changing and I must say that I'm pleased with the way it is. After 28 months, the AA portfolio is ahead of SPY by 3.18%. The current allocation plan was implemented in June 2007, prior to that the AA portfolio was under performing SPY by about -3% as my market timing in early 2007 proved disastrous. In other words, the AA portfolio outperformed by over 6% last year while keeping the volatility low.

In keeping the same asset allocation, perhaps the most difficult thing to do is to sell the leaders (PM, commodities and emerging markets) and buy the laggards (small cap, REIT and private equity). The last (PSP) was especially difficult to justify since one can argue that the shares of private equity companies bear little resemblance to the returns enjoyed by the principles, not to mention a much tougher credit environment. I'm stomaching the 5% allocation for now while hoping the market has discounted most of the risks. We'll surely revisit this topic in a year.