Kill Your Beta To Save Your Alpha

Includes: IYR, SPY
by: Nicholas Donohoe

It can be easy to forget that our portfolio of stocks has two drivers of return, alpha and beta. Often we get so caught up in the excitement of stock picking we forget that it's the beta that can really do the harm. This article will help you take a more active role in controlling the beta of your portfolio by aligning it with your macro market opinion.

Beta is a statistical metric that has a couple of interesting interpretations. But put the math aside for now and just remember that beta means exposure. So if our portfolio has a beta of 1.25, that means we have the equivalent of 125% of the benchmark exposure. Essentially beta transforms the risk of our portfolio into benchmark terms like a currency exchange. This is helpful because using beta we can easily quantify our exposure to a single risk factor.

Because of the CAPM, the most common beta risk factor in practice is the market portfolio, typically represented by a broad index like the SPDR S&P 500 (NYSEARCA:SPY). But using beta allows us to easily construct a single factor risk model in which we can explain our portfolio returns in terms of any other asset too, not just the SPY. We don't always have to convert to the market portfolio 'currency'. We could just as easily quantify our risk exposure relative to real estate by converting our portfolio exposure into iShares US Real Estate (NYSEARCA:IYR) units, rather than SPY.

Here's our game plan. The first step will be to define our market outlook over the next few months to a year. Next we will quantify our portfolio exposure to a single risk factor by calculating our beta. Lastly, we make any necessary trades to ensure that our market forecast from Step 1 matches our risk exposure that we calculated in Step 2.

For now, let's take it as a given that you have an overall market outlook and focus on making sure that forecast and your portfolio risk exposure are in line. To do that we need to know our starting portfolio beta. There are few ways to calculate it. You may be able to get the information from your EMS (trading system). If not or if you want to be able to select a different risk factor (other than SPY) you will probably need to use a portfolio analytics tool. As a last resort you could calculate it in Excel because some financial sites (like Yahoo! Finance) have a pre-calculated Beta in the summary. Since beta is portfolio additive, you could look up the beta for each of your holdings and calculate the simple weighted average.

Here's an example of what we have discussed so far. First we need a sample portfolio. I entered 7 of my favorite stocks into an APT optimizer along with some ranked alpha estimates. I set the min/max holding constraints to 10% and 25% respectively. Below is the max IR portfolio with at least the mid-rank alpha minimum. We will use this as our sample portfolio going forward. For benchmarks we will use the classic S&P 500 (a portfolio 100% invested in SPY) and to illustrate an alternative risk factor I created a Real Estate benchmark (a portfolio 100% invested in IYR).

Let's check the beta exposure of our sample portfolio to each of the 2 benchmarks.

Below is our portfolio beta vs the S&P 500 benchmark.

Below is our portfolio beta vs the Real Estate benchmark.

So we can see that beta depends a lot on the risk factor we select. We can interpret the most recent beta estimates for each as follows. In the case of the SPY risk factor, our portfolio beta was 1.21, so we have the equivalent of 121% of SPY exposure. If our portfolio is worth $100,000, then our risk is equivalent to us having $121,000 of SPY. Conversely, using the IYR risk factor our beta is .39 or 39% of IYR exposure. If our portfolio is worth $100,000, then our risk is equivalent to us having $39,000 of IYR.

Now that we have defined our beta exposure to our preferred risk factor we need to review our adjustment options. Since we are going to be beta hedging, we need something to hedge with. Assuming you selected the S&P 500 as your beta risk factor, there are a few options. The best choice is to use futures. The required margin and trading costs are extremely low. The biggest drawback however is the exposure size. At the time of this writing, one E-mini S&P 500 contract carries an exposure notional of about $89,000. You may also have to roll it depending on how long your hedge is active.

If you don't trade futures or the exposure size is too big you have other options. The most straightforward way is to sell short SPY. You could also use options. Even a very basic vertical strategy could be easily employed to adjust your beta using very little capital. Lastly, if you don't want to use derivatives and you can't sell short you could purchase an inverse ETF like ProShares Short S&P500 (NYSEARCA:SH). In this case you will have to make an adjustment for the amount of capital you use to hold the position which will depend on your trading account's margin requirements.

Let's take an example and suppose that at the end of May 2007 we were getting increasingly nervous about real estate and therefore the market overall. There were quite a few people coming out saying real estate was in a historic bubble and that they couldn't keep loaning money to people who didn't have any for much longer. One sensible thing we could have done is killed our real estate beta and left the rest of our portfolio alone. Our portfolio beta vs the IYR at the end of May 2007 was about .50. So if our portfolio was worth $100,000 at the time, a beta of .50 meant we were carrying equivalent real estate exposure of about $50,000. Our beta hedge would have been to sell short $50,000 notional of the IYR. This trade would have taken our IYR beta down to near zero. Let's check to make sure it worked.

Had we done this on June 1st, 2007 and reversed the hedge of June 1st, 2009, here is how it would have worked out for us.

This simple example shows the power of being able to quantify your portfolio risk exposure and adjusting it to match your market forecast. In the example, we reduced our beta to a different benchmark, the IYR. Had we taken down our beta to about .5 vs. the SPY we would have had almost identical results. Although in the example we took down our entire beta with respect to the real estate index, I don't generally recommend taking down S&P 500 exposure by that much. The real estate hedged portfolio still had an average beta with respect the SPY of between 0 and .5 over that time period. Also keep in mind that in either case we had our hedge on the wrong way about 50% of the time. We put it on about 6 months too early and removed it about 6 months too late over the course of a two year span and still we experienced an average of 13.5% alpha per year vs. unhedged. So remember you don't have to have the perfect market timing call to benefit from this strategy.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.