Archive for the ‘Quantitative Equity’ Category

Hunting for negative beta

February 9th, 2009 1 comment

In my previous post on “absolrelative” performance, I spoke about absolute return and relative return, and how a money manager’s performance should be measured by one metric or the other, but never by some combination of both. Getting relative return is quite straightforward (well, not entirely, as you’ll see in my later post on the importance of the benchmark) – you invest in the benchmark, and then over-weight the stocks you think will out perform. That way you, theoretically, add value through your stock picks, while not missing out on general market movements exhibited by your benchmark. In this post I’ll talk about what you need to do to earn absolute return – that is a positive return no matter what the market does.

To fully appreciate the hunt for negative beta, it’s important to understand what beta is (besides short-form for a member of some collegiate fraternity or sorority) and how it fits in to stock returns. As mentioned in What is the Y-Factor?, investors require compensation for holding risk. For example, investors who buy IBM stock expect a return based on the risk associated with IBM. That risk (and thus the return investors demand) can be decomposed into many things: the risk of the economy slowing and computer sales falling, the risk of IBM’s products becoming inferior to Dell’s products (thus hurting sales), the risk of IBM going bankrupt, etc. In the quantitative equity world, we call each of these risks a factor. So, each stock has some exposure to any number of risks, and each risk carries some compensation with it. In quantitative finance, we call the exposure of an asset to a particular risk it’s beta (β) with respect to that risk.There are many kinds of risk that investors may require compensation for. The most notable are: risk related to the market (how much more or less risky is a particular stock than the whole market), risk associated with the firm’s size (small firms tend to be riskier than large firms), risk associated with liquidity (more liquid assets – those that trade more often, are more transparent, and have a well established price – are less risky than more illiquid assets). A typical stock will have a beta for each risk. Note that there are two general types of risks inherent in the examples I mentioned: IBM specific risk (such as it’s products being inferior) and general market-wide risk (such as the economy slowing - which effects all firms, not just IBM). The former, firm-specific type of risk is called idiosyncratic risk, and the latter, general risk is called systematic risk. Systematic risk drives all asset prices (i.e. the risk of the economy failing is priced into all stocks, which is why you see all stocks generally fall when bad economic news comes out), whereas idiosyncratic risk drives only specific firm prices (which is why only IBM would fall if IBM were to report bad earnings). Of course you may see Dell stock fall when IBM reports bad earnings – this is because investors may perceive an industry-specific risk: whatever it is that hurt IBM earnings may also hurt Dell earnings (i.e. maybe computer are becoming deprecated so all players in that industry suffer).

We can take the lesson we’ve learned – that the returns that stocks earn represent the risk associated with the stock – and apply that to a portfolio as well. Since a portfolio is simply a collection of stocks, the return of that portfolio is simply the aggregate of the returns of each stock within the portfolio. Thus, since each stock return can be theoretically decomposed into risk factors, the sum of all stocks (i.e. the portfolio) can also be decomposed into risk factors. So, if a portfolio is simply compensation for carrying risk, what do we pay portfolio managers for? Surely if all they are doing is taking my money, putting it at risk, and earning a reward for that risk, I should be able to do the same thing myself, right? Not exactly. If you want a portfolio that has the risk profile of the S&P 500 (the aggregate risk of the 500 largest firms in the U.S.), you could simply invest in an S&P 500 index fund. However, you could also hire a portfolio manager to manage your money relative to the S&P 500. This means that he/she would generally take the same risk (and thus earn the same return) as the S&P 500, but should earn you even more by utilizing his/her skill to pick more stocks that will go up and fewer that will go down. The astute reader will realize the contradiction here: even if the portfolio manager picks more stocks that go up and fewer that go down, aren’t they really just picking more risky stocks and fewer of the lower-risk stocks (since risk and return are joined at the hip)? Well, in a way, yes, that may be true. However, you can argue that the portfolio manager’s skill is that he/she knows which risk to take at which time so as to not lose money. The other dimension to this is that the whole framework I’ve laid out is very theoretical – it assumes that assets are always priced to reflect all the risk they are exposed to. This is the (simple) definition of an efficient market. However, practically it’s not possible to know all the risk that any particular stock is exposed to, and it’s not possible to know exactly how to price each risk. Additionally, there are many other issues at hand that reduce the efficiency of the market, such that not all return is compensation for risk. A portfolio manager should be able to capitalize on these inefficiencies and make the investor money in doing so. It is for these skills that money managers should be compensated – they should not be compensated just for taking risk (though unfortunately that’s more often the case than not).

Okay, so we’ve established that the return of a portfolio is made up of the risks in that portfolio, plus some additional return generated by the portfolio manager’s ability to pick stocks. We can characterize this using the equation:

E[R] = α + β1γ1 +  β2γ2 + … + βnγn

where E[R] is the expected return of the portfolio, βi is the portfolio’s exposure to risk i (where i is a number – remember that a portfolio is exposed to many risks, so i is a number from 1 to the n, where n is the number of risks in your model), γi (γ is the Greek letter gamma) is the compensation for risk i (so that the product βiγi is the total return you get for taking risk i – for example, if IBM has an exposure of 0.9 to the economy and the compensation for risk to the economy is 2%, then IBM should earn 0.9 x 2% = 1.8% return for its risk exposure to the economy), and α (the Greek letter alpha) is the value added by your portfolio manager above and beyond any risk being taken. As you can see from the equation above, if you want to eliminate all risk in your portfolio, you have to eliminate all the βs. This will leave you with an absolute return portfolio – one that earns α% each year, no matter what.

So, getting the absolute return part of the absorelative performance we’ve been asked for at work is quite easy – just get rid of beta by finding things with negative beta and adding them to the portfolio in just the right quantity so that the overall beta is zero. Piece of cake – well not quite!

There are a couple of ways to get negative beta: 1) sell (or rather short) assets that have positive beta, or 2) buy assets that have inherently negative beta (imagine an asset that loses money when everyone makes money, and makes money when everyone loses money). These two approaches can be implemented many ways – for example, you can either short individual stocks, or short ETFs, or short futures – all of these are variants of selling assets with positive beta. To buy assets with negative beta, you can buy “short” ETFs, or buy other assets (for example, if your portfolio is exposed to oil prices sinking, you can buy oil so that when your asset loses value, your oil position makes money, effectively mitigating the risk).

Since I work for an insurance company – a business that’s typically conservative in nature, and required to be conservative by regulation – we can’t do any of option 1 (short assets). So, we can’t short stocks with similar beta exposures to the ones we hold in our portfolios. We also can’t (directly) short the market, or short anything else. This is a major limitation when considering absolute return strategies. For example, suppose our models predict the best stocks from each industry and we buy those. Next, suppose that we’re greatly gifted in our stock picking ability and that one of our picks, a bank, does very well – it has earned 5% by June, whereas all other banks have earned about 1%. Now, suppose that financial services suffers great losses for some reason (lets go with a wild situation here – suppose credit freezes up). All investors are afraid of holding banks, and so bank prices immediately fall 10%. Though we picked the best bank, it is still not free from the fear of banking running through our hypothetical market, and our pick is now earning -5% (whereas all other banks are at -9%). You clearly see the problem here – since we can’t eliminate the risk of being a bank and just isolate the return associated with this particular bank, we’re always prone to losing money when the market tanks. (A hedge fund could, on the other hand, short the risk of the banking sector since they can go short, thus isolating the return derived from the quality of it’s pick).

Additionally, since we’re equity managers we can’t exercise option 2 fully. That is, we’re not able to buy other assets (like commodities, fixed income, or other things) that may serve as an effective hedge. Also, we’re not allow to use derivatives to hedge our position since we can’t use them for speculation.

So, the only option we’re left with at this time is using the emerging class of short ETFs. These securities are designed to deliver you a return equal to the negative of whatever it is you’re targeting. For example, suppose you want to short banks as in the example above, there are now ETFs available that you can buy and earn a return that’s negative to the banking sector (if banks go up 5% today, you go down, and vice-versa). This is great! Technically we’re “long” the asset – we bought it with our money, yet it gives me negative beta! So, now we can use some weighting of the various short ETFs (they have one for just about each major industry and the market in general) to neutralize most of the beta in our portfolio. Note, that it’s not possible to neutralize allof the beta – these short ETFs represent industries in general and will never allow you to short all the minute risks of individual firms. The only problem with this approach is that it’s very capital-intensive. If the investors give me $1,000 to invest, I can only invest about half of it since I have to spend the other half buying negative beta. So, if I generate 4% α each year, I’m only doing it on half of my portfolio so my return for the entire $1,000 is really only 2%. This is verycostly! Of course, if absolute return is what I’m after, this is the price that must be paid given all the other constraints on us (i.e. no direct shorting). There are other options available, but they require me to delve into derivatives, so I’ll defer to another post.

 So, though we can’t construct a portfolio that is truly risk-neutral, we can get pretty close using short ETFs. You’d basically pick the stocks your model predicts will out-perform. Then find the weight of your in each sector, and finally buy a proportionate amount of the short ETF to eliminate that weight. You’ll still be prone to some risks, but the major market movements should be covered. However, keep in mind that you now have an absolute return portfolio. So, if the market moves up 25%, you’ll miss out on that whole move since your short positions will offset any gains made by the long positions. This does allow for a cool feature called portable alpha, which I’ll talk about in another post.

Absorelative performance

January 13th, 2009 5 comments

No, it’s not a typo… “Absorelative” is the term I’ve coined for what we’ve been tasked with at work for the year 2009. Our mission is to earn an absolute return, unless the market moves up, in which case we’re expected to deliver a relative return – so we’re looking for a mix of absolute and relative performance, or “absorelative performance”. Basically, this means that if everyone loses money, we must not. But if everyone makes money, we too must make money.

To better understand the implications of this, it’s important to understand how money manager performance is measured, and how managers are compensated. Basically you can measure how your investment manager is performing in one of two ways: absolute return, or relative return. Absolute return is the total return of your portfolio. If you give someone $1 million to invest and they give you back more than $1 million at the end of the year, then they have earned a positive absolute return. Likewise, if you get less than $1 million, they have earned a negative absolute return. The fact that other investments (such as a passive index fund) could have earned 30% or lost 30% is completely irrelevant – your manager gets paid if he/she makes money. Relative return, on the other hand, depends on a benchmark. Suppose you want your manager to invest in large U.S. company stock. An appropriate benchmark could be the S&P 500 – an index of the largest 500 U.S. companies, which  you can invest in yourself – it’s pretty easy and cheap. So, you only want to pay your manager if he/she is able to beat what you can earn yourself – that is, beat the S%P 500. If the S&P 500 earns 25% and your manager earns 28%, then he/she has earned a 3% relative return. If he/she earns 22%, he/she has earned -3% relative return – he/she has still made money, but he made less than the benchmark, and so shouldn’t get paid. Clearly, the best compensation structure for you depends on what you’re looking for – if you want exposure to a particular asset class and are open to its risk and return, you want to set up a relative compensation structure – only paying your manager for picking those names that are better than average. However, if you’re looking to minimize risk and just want positive growth, an absolute structure is probably a better fit – an often small, but positive, return with very little chance of losses.

Certain types of money managers typically have certain kinds of compensation. Hedge funds can go long and short (that is, they can buy assets they think will make money, and borrow and sell assets they think will lose money, expecting to repurchase the sold asset later at a cheaper price to repay the loan, and keep the difference between the sale and repurchase prices), and so typically employ strategies that can profit in up markets and down markets. These strategies should make money no matter what, and so are called absolute return strategies. As you would expect, since hedge fund managers employ absolute return strategies, they are typically compensated on an absolute return basis.

Traditional money managers (think of insurance companies, mutual funds, etc) aren’t allowed to go short, and so can only buy whatever asset class they are managing (bonds for bond managers, stocks for equity managers). Thus, if you’re a long-only equity manager, and stocks are falling, your portfolio will fall too since all you can do is buy the falling asset class. The performance of these strategies is tied to the benchmark, and so they’re called relative return strategies, and the manager is compensated relative to some benchmark.

Getting back to the situation at work… Allstate is an insurance company, and as such we’re a long-only shop. Until now our performance has been measured on a relative basis. In 2008, equity markets fell sharply, as did our portfolios. By definition, if we beat our benchmarks we should still get paid, and if not, we shouldn’t. As you can imagine, the investors who give us capital may not be thrilled with this setup. On one hand they were looking for exposure to equities (and by that I mean the risk and return that comes with equities), and should be glad that we were able to provide a return greater than, albeit still negative, the benchmark they had selected. On the other hand, when 35% of your portfolio disappears, it’s hard to be excited and pay your money manager for making you one third poorer than you were at the start of the year. So, going into 2009 things changed – the investors decided that they didn’t want to take this much risk, and that they didn’t want to pay their managers if they lost money – all the ingredients of an absolute performance setup. (As a side note, I would have argued that if the investors aren’t comfortable with the risk of equities, the simpler, more direct solution is to simply not invest in equities. They should invest in a safer asset class. However, this is a suicidal argument for me since if the investors choose not to invest in equities, I’d be unemployed!)

Earning an absolute return in itself is not a big issue – see my upcoming post on negative beta. The problem comes in when the investor wants the relative dimension as well – when the investor says “don’t lose money, but if the market is up x%, you must be up about x% too”. The issue here is that in order to get absolute return, we have to eliminate all beta exposure (market beta, size beta, style beta, sector beta, etc). This way, no matter what happens in the markets, our stocks earn only alpha – their unique return after accounting for all systematic risk. This is a great positive in down markets – in fact zero beta is what allows us to not lose money (assuming we’re right about our stock predictions – our alpha). However, not having this beta exposure in up markets means that your portfolio is missing out on systematic return. That is, if everyone feels more confident about things and stock markets recover, you’ll miss the recovery because it is market-wide compensation for positive sentiment, not company-specific compensation. Thus, you will under-perform the market in up markets.

So, given that we can’t earn absolute return by neutralizing beta since that also eliminates our return in up markets, the only choice we’re left with (as far as I can see) is to be in stocks in good times (so that we’re earning alpha and beta), and be in cash (or cash equivalents) in bad times so we’re not losing money tied to our stocks’ betas. This strategy is called market timing, and it’s something that no manager that I’m aware of has ever been able to do consistently and successfully. Basically you have to know more often than not when the market will go up so you can buy stocks, and when it’ll go down so you can sell stocks.

Now, my friends, you understand the dilemma for 2009. In the absence of a crystal ball that tells us what will happen in the markets tomorrow, how do we know when to switch from stocks to cash? If you have any ideas, or see something I missed, please leave a comment and educate me. In the mean time, I’m going to roll my dice – even means market, and odd means cash!