Monday, April 14, 2008

More on Excess Returns

If you can estimate your portfolio beta it is pretty simple to compute your excess return:

In the equation, e(t) is the percentage excess return in month t. r is your portfolio return, m is the market percent return given by your benchmark index, and f is the risk free rate. The normal return is a mix of the market return and the risk free return weighted by beta. I use the MSCI index as my benchmark. Specifically, the All Country Gross Index. Make sure when you choose a benchmark to include dividends. The net and gross MSCI indices do include dividends - the gross is pre-tax and the net post-tax. Total return data for the S&P 500 can be found here. I use the 90-day Treasury Bill rate as the risk free rate (you'll need to compute the monthly rate from this annual rate).

You can estimate beta in more or less sophisticated ways. If you are 100% in stocks and guess your stocks are average and you are using no leverage, you can use a default of one. In this case, the excess return is just your return minus the market return. A more sophisticated approach is to compute the weighted average of the betas of all your stocks and funds, which you can find on Yahoo Finance for example. More sophisticated still is doing some kind of regression analysis - you need a track record of your monthly returns to do that. My preferred method is a time series model that allows my alpha and beta to vary over time.

To find how much your actual excess income is per month, you then need to multiply the percentage excess return by your net worth. I've done it here, using the S&P 500 as the benchmark:

The bars are the monthly "risk-adjusted excess incomes (or losses)" while the light green line is the total of the last 12 months. A strong cycle is very clear - I've gone through periods of above and below par performance fairly regularly. Alpha smoothes all this out into an estimate of the average excess return. The following chart does this using the MSCI instead as the benchmark:

There is no guarantee though that this level of performance can be maintained. The huge fluctuations on the SPX chart above make that clear. In this post, I was wondering out loud whether I could maintain that performance in the coming year by looking at where the returns would come from. I wasn't saying I could maintain that indefinitely. I don't know.

4 comments: said...

Are you only analysing your USD returns, or is there some AUD returns included? Even if you are converting all the final figures into USD values, wouldn't your weighting towards AUD denominated equities mean that the US 90-day treasury rate isn't a totally appropriate proxy for your risk-free rate? Perhaps you should be using a weighted average of the US rate and the AU equivalent for your calculations?

I'd be interested to work out my own "alpha" - but unfortunately my paperwork for my investment history isn't up to scratch. I have enough trouble working out my CG for tax returns, and only have a "ball park" estimate of my overall rate of return ;)

mOOm said...

The returns are the total portfolio returns measured in USD. A couple of years ago the the US and Aus rates were pretty close. They aren't now obviously :) That begs the question: "what is the appropriate risk-free rate for a global investor". If your beta is one, then the choice of risk-free rate doesn't matter as you deduct it from both your own and the market's return and it has no effect on the results. As beta deviates from one it'll make a bigger and bigger difference.

Michael Sean Anderson said...

Great site. Have not started trading, but am considering. One vital issue for me is the accurate representation and tracking of account values and performances (long term success is never an accident).
I found your link via a recent comment at traderfeed. Very grateful to find guidance in calculating and understanding running valuations in global context.
Best Regards,

mOOm said...

The key thing is to know how much you are making pre-tax each month from investing/trading. Most people don't know this number. Once you have that data you can easily compute anything else you like. All you need to do is keep a record of portfolio value each month and how much you put in and out of the investment accounts. To get accurate pre-tax numbers any tax deducted at source also needs to be accounted for.