Monday, January 9, 2012

Distilling alpha with factor betas

One of the hardest questions any portfolio manager has to answer is, "What can go wrong with your strategy?" If he doesn't know, then it's a sign that he hasn't fully thought out all the nuances of his investment approach.

How to untangle alpha using factor betas
Here is one example of how I used to evaluate investment strategies when I worked at and with hedge funds.

A couple months ago, we were approached by an experienced bond portfolio manager with an idea for a bond strategy for the Canadian market. The idea involved overlaying a call option writing strategy on the US Treasury market on top of a Canadian bond portfolio. The resulting portfolio had the following benefits:
  • Same duration exposure as the benchmark, i.e. no significant interest rate directional bets;
  • Higher credit quality compared to the benchmark
  • Significantly higher realized return than the benchmark
I interviewed the portfolio manager and found out that the most significant risks of the strategy are, in no particular order:
  • Basis risk between the US and Canada yield curve
  • Currency risk
  • Volatility risk as it relates to option pricing

Disaggregating the alpha using factor betas
He had been running a "live" paper portfolio in real time for a little over a year. The backtest looked good as it added an alpha of over 3% in that period. Given my assessment of his risk exposures, I wanted to see whether the outperformance was the result of a favorable factor beta exposure, i.e. the strategy bet on a certain kind of exposure and it worked, or the alpha was relatively independent of factor beta.

We got the weekly returns of the paper portfolio and I made the following table:

I averaged the weekly alpha of the strategy under different scenarios. On the first line, I asked, "What is the average weekly alpha when the US long bond price is up, down or relatively flat?" In that case, the strategy underperformed when the long bond rallied, largely because it was selling call options at the long end of the yield curve and the premiums weren't enough to offset the gains in bond prices, and outperformed when the long bond price was either flat or falling.

Similarly, I performed other forms of scenario analysis. What happens to the alpha when the Canada and US curve diverge? What happens when implied stock volatility (I didn't have a good proxy for bond volatility) moved up or down?

Stress testing factor beta exposures
I used scenario analysis to project an annual alpha. The average case analysis assumes a Gaussian distribution where 50% of the time exposure to that factor beta is neutral, 25% of the time it is favorable and 25% of the time unfavorable. Using the example of the long bond price factor, I calculated an expected alpha assuming that 25% of the time, the bond price was falling, 25% of the time it was rising and 50% it was neutral. In this case, that came to an expected alpha of 3.90% per annum.

I wanted to stress test the strategy some more. What if the market gods aren't with us?

In the second column labelled "Adverse Case", I assigned weights of 50% neutral, 33% unfavorable and 16% favorable. Using the example of the long bond price factor, the expected alpha came to 0.80% per annum.

What happens if a catastrophic scenario? In the third column labelled "Worst Case", I assigned weights of 2/3 neutral, 1/3 unfavorable and 0 favorable. (Remember that these are weekly alphas and it would be difficult to believe that, in the case of the long bond price, it would fall for a single week in an entire year and would be rallying 17 weeks out of 52 weeks in the year.) The expected alpha in the worst case analysis for the long bond price factor came to -2.13%.

Putting it all together, the strategy looked pretty good. We could expect an alpha in the order of 3.0-3.6% a year - which is an astounding figure for a bond portfolio. In a typical bad year, we could still expect outperformance of 0.8% to 1.8%. If the roof caved in and everything went wrong, alpha deteriorated to between -2.1% and a positive 0.2%.

This is an example of a simple method of evaluating any investment strategy using scenario analysis with factor betas. This is another way of asking the question, "What can go wrong with the investment strategy and how badly could things fall apart?"

Ultimately, we passed on implementing the strategy not for investment reasons, but for business ones. If anyone is interested in further details or in funding such a bond strategy, please contact me at cam at hbhinvestments dot com and I will be happy to refer you to the bond manager.

Cam Hui is a portfolio manager at Qwest Investment Fund Management Ltd. ("Qwest"). This article is prepared by Mr. Hui as an outside business activity. As such, Qwest does not review or approve materials presented herein. The opinions and any recommendations expressed in this blog are those of the author and do not reflect the opinions or recommendations of Qwest.

None of the information or opinions expressed in this blog constitutes a solicitation for the purchase or sale of any security or other instrument. Nothing in this article constitutes investment advice and any recommendations that may be contained herein have not been based upon a consideration of the investment objectives, financial situation or particular needs of any specific recipient. Any purchase or sale activity in any securities or other instrument should be based upon your own analysis and conclusions. Past performance is not indicative of future results. Either Qwest or Mr. Hui may hold or control long or short positions in the securities or instruments mentioned.


Ivo said...

Did you do your factor beta evaluation, based on the factor movements during the last year only? Maybe the factors did not really move adversely enough over this short time window?

Ivo said...

Did you use the factor movements only over the last year? Maybe they were not big enough over this short time frame.

Cam Hui, CFA said...

Yes I did, but that's all I had to work with.