Tuesday, April 08, 2008

What Does Alpha Really Mean?

In my recent posts analysing Madame X's portfolio I used various indicators to assess the performance of mutual funds. One, alpha, is the "risk adjusted return relative to the benchmark index" we are comparing the fund to. We use regression analysis to find how much the monthly percentage returns of the fund respond to the percentage returns of the index. For example, the fund might return -4.3%, -1%, and -0.2% for the first three months of this year while the S&P 500 returned -6%, -3.25%, and -0.43%. Clearly, the fund did a lot better than the index, but how much of this is due to being less invested in the index and how much is unrelated to the market? A simple regression (same as fitting the best straight line when the fund returns are on the Y axis of a graph and the index returns are on the X axis) shows that for a 1% rise in the index the fund only goes up 0.73%. In other words this fund is taking on only 73% of the market return. The intercept term on the Y axis, or regression constant, is 0.54%. This tells us on average how much return the fund derived from other sources, such as manager skill in timing and security selection per month. For a whole year, this works out to 6.6%. This number is "alpha".

But what does that really mean? One way to look at this is to imagine investing 73% of your money in the S&P 500 index and 27% in 90 day government bonds (T-Bills) - this is a passive investment with the same amount of market risk as the fund in question. The average difference between the return on this investment and your returns from investing in the fund are "alpha". If you invest $10,000, this manager will deliver you additional income of $660 per year above what the risk-adjusted passive investment will return you. On average. There will be months and years where he or she will produce higher or lower excess returns.

I routinely compute my own alpha relative to the MSCI All Country World Index and S&P 500 (with all dividends reinvested in each case - the total return indices). Against the S&P 500 my advanced time series model (Kalman filter) estimates my beta at 0.87 and my alpha at 17.8%. Our net worth is currently $464,000. This means that I am earning $82,500 a year above what I would get from investing 87% of our money in the S&P 500 and 13% in T-Bills. A regression for just the last 36 months gives an alpha of 10.23% or $47,500 per year. Returns relative to the MSCI are not as spectacular - ranging from $24,750 to $44,900. A big caveat is that this past performance may not continue going forward, but it gives some idea of the value derived from actively investing instead of passively investing. If you actively manage your portfolio you should ask a similar question about how much value you are adding.

The nice thing about investing/trading is that these returns can scale up. There is no reason why I couldn't do exactly the same thing with several million dollars instead at some time in the future. This is one of the reasons that trading is an attractive career option to me.


BackOfficeMonkey said...

Hey Moom,

Just a quick comment about Madame X' portfolio and her negative alpha. I just took a peak at her portfolio and she isn't solely invested in large cap core but rather a range of different asset classes so I don't think the S&P 500 is a good independent variable for the regression (would you run a regression on the S&P500 against the an active int'l equity fund? of course not).

Anyways I think to find her true alpha its simply the weighted average of all the tracking error of each individual fund/investment vehicle against their predefined benchmark.

Her true measure of investment success is how the portfolio measures up against her net present value of all her future retirement liabilities.

Anyways if your running your own investments like an absolute return hedge fund I would not use the S&P 500 as its benchmark rather something like 90day t-bill+5%.

Best of luck.

mOOm said...

I didn't compute any kind of overall statistics for Madame X because I don't know when she bought anything and so have no data. I assessed each fund one by one and relied on the data that given by Yahoo unless it looked grossly inaccurate to me.

On my own results, I don't really take the SPX results seriously. I use the MSCI World All Country as my benchmark as I am invested globally though most in Australia. My current exposure to the stock market is a beta of more than one. So seems an equity benchmark makes sense? It's what I'd probably invest in if I wanted to spend as little time as possible on the task. I try to add value to that by short-term and long-term trading and investing with what I think are quality managers. I estimate my alpha is between 5-10% depending on the estimation method used.

BackOfficeMonkey said...


Sorry I miss-read your post! 6.6% alpha is pretty good, was the t-test significant @ .005?

I guess i'm sort of wary about your portfolio structure is because I look at portfolios of endowments/ foundations and pensions all day and they do things differently. Its all about asset classes. We like to think in the box and produce mediocre returns, lol!

Personally I invest my money based on an investment thesis of how I see the world 40+ years down the road and the process of getting there. Short term disturbances are just rebalancing opportunities to me. Gez I sure hope i'm right down the road.

mOOm said...

6.6% was just an example from a regression with just three data points. For my own results the regression constant for a 36 month sample is not significant - the t-stat is 0.95. My information ratio for the last 36 months is 1.3 which is a little more significant. However, the constant for the last 60 months has a t-stat of 1.82 which has a much higher level of significance (annual alpha 11.6%) and the information ratio is a highly significant 2.53.

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