Arnold Kling  

Why Derivatives?

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A reader asks.


why would one consider hedging/derivative strategies, e.g., longs and shorts, collars and arbitrage? Stated differently (I think), a long term buy and hold of this assumed portfolio would seem to maximize its return without these hedging strategies. Yet the sense I get from the portfolio literature is that even for a modest investment return objective (whatever that may be), one can increase this modest return without increasing risk by replacing a portion of the assumed portfolio with some hedging type assets. What's the risk theory here?

In the capital asset pricing model, you optimize risk-return by holding a diversified portfolio. Derivatives are redundant assets. I think that is the path that Fischer Black took to deriving the option pricing formula. I think he started out wondering why anyone would use derivatives, but he ended up in a different place (a cynic could say that the different place was Wall Street, which profits from derivatives).

One could argue that in the real world there individuals face institutional constraints on portfolio diversification (for example, your wealth is closely tied to a single firm). In addition, firms face bankruptcy costs, so that they do not follow Modigliani-Miller. Given those constraints, there is a role for derivatives in mitigating the risks that imperfectly diversified agents would otherwise have to bear.

However, it is my view that if you look closely enough, you will see derivatives used primarily either to reduce transaction costs (as in stock index futures, which allow you to trade a basket of stocks more cheaply) or for regulatory arbitrage. One of the big mistakes that regulators made during the mortgage securities boom was to view derivatives as creating a new world of risk management. The novelty was in evading capital requirements, not in making banks fundamentally safer.

P.S. I can tell from the early comments that if you don't know the capital asset pricing model you won't understand this post. CAPM is one of the most difficult concepts to explain I have ever encountered. Past attempts here and here.

I strongly recommend going through the effort to try to understand CAPM. I think it is very insightful.


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COMMENTS (14 to date)
Rohan writes:

I'm not a super-financial person, but I work in the industry as a software dev, so maybe I can explain why one would hedge in a simple manner.

The point of the basic long/short hedging strategy is to filter out extraneous influences on what you are investing in.

Like, let's say you're an American, and you invest in a Canadian company because you think it is a good company. If the company does well, but the USD-CAD exchange rate moves sharply, the value of your investment can go down even though what you are actually investing in performed well.

Buying some CAD currency as a hedge allows you to filter out the exchange rate changes. If the exchange rate goes up, you gain X dollars on your investment, but lose X dollars on your currency hedge. If the exchange rate goes down, you lose Y dollars on the investment, but gain Y dollars on the currency hedge. No matter how the exchange rate moves, you don't lose or gain money.

So hedging allows one to eliminate certain risks, in this case the risk from the exchange rate, that just a long term buy and hold position would have. And that risk can be substantial. In the past 10 years or so, the CAD rate risen from 0.7 to 1.0. Depending on what you invested in, that might have turned a strong performance by the company into a net loss for you.

biagio writes:

I agree with the previous comment and I am bit puzzled by the post and the question in the post.

Derivatives ARE primarily risk management tools (which, I agree, should be used judiciously). A derivative is a synthetic instrument that allows the user to gain exposure to a market variable without actually taking possession of it. This means that when purchased in the opposite direction with respect to our main investment it filters out sources of risk (like the FX example above).

The way I see it is in terms of Taylor series. Imagine that you have a function plus a constant and from that function plus a constant you start subtracting one by one the terms of the Taylor series corresponding to the function. The more terms you subtract the more you'll be left with something similar to the constant. The constant represent the more or less complicated return you expect from your investment: this return is governed by things beyond the capital markets. The terms of the Taylor series corresponds instead to the derivatives used to fend off the risks that are governed by the capital markets.

Ken writes:

I think you need to make a distinction between derivatives that have option-like features and those that don't. Options are NOT perfectly replicable by non-option instruments. Black-Scholes showed that they are replicable given certain assumptions including, importantly, no jumps in asset prices, i.e. continuous trading at continuous pricing. (Another assumption is no transaction costs, but you refer to that assumption in your post I suppose.) Options are extremely useful risk-management tools in certain situations and can't be reliably or easily replicated with non-option instruments.

To be clear, Arnold might very well be right that MOST derivatives are used for non-option purposes. I don't know the numbers...

Radford Neal writes:

Rohan: So hedging allows one to eliminate certain risks, in this case the risk from the exchange rate, that just a long term buy and hold position would have.

That assumes that the exchange rate moves don't reflect actual changes in the relative purchasing power of the currencies. There does seem to be some of that (for reasons that aren't clear to me). But really big moves in exchange rates are likely to be due to actual changes in relative purchasing power. If you invest in a Canadian company, but hedge the currency "risk", you've actually added to the risk in some scenarios. For instance, if the US, but not Canada, experiences hyper-inflation, an unhedged Canadian investment will keep its value, but a hedged investment will end up worth nothing.

GIVCO writes:
For instance, if the US, but not Canada, experiences hyper-inflation, an unhedged Canadian investment will keep its value, but a hedged investment will end up worth nothing.

Yes, but you are talking about a company-currency parlay bet; if you don't want the parlay, bet on the Company and hedge the currency. In a parlay, you lose the whole bet if one leg fails.

I don't know CAPM, but I know that my 12-1 future on the Mavs winning the NBA title was looking good after the semi-finals, but a small play on OKC in the 2011 W.C.F and on Miami in the Finals (a hedge) guaranteed a pay day.

You also buy this stuff for illiquid investments, to refine specific bets that may suffer by sector changes, to collar lock-ups and, of course, for the sheer fun of it. Never underestimate that.

Mark Little writes:

On CAPM, see Eric Falkenstein. (http://falkenblog.blogspot.com/) He has lots of interesting things to say about risk management more generally too.

If you do believe in risk/return tradeoff, Markowitz is a good source. I once heard him give a talk on his mean-variance model, and for a while he had me totally convinced.

I agree with Arnold:

However, it is my view that if you look closely enough, you will see derivatives used primarily either to reduce transaction costs (as in stock index futures, which allow you to trade a basket of stocks more cheaply) or for regulatory arbitrage. One of the big mistakes that regulators made during the mortgage securities boom was to view derivatives as creating a new world of risk management. The novelty was in evading capital requirements, not in making banks fundamentally safer.

(Not my ideas; Arnold has me convinced, and I've stayed convinced.)

PrometheeFeu writes:

@Rohan:

That would change your risk-return profile though. If you eliminate the risk from the foreign-exchange losing you money, you also eliminate the risk of it making you money.

The only way I can imagine a derivative decreasing your risk without also decreasing your return would be if the derivative hedged against a risk that was correlated with your portfolio but had a less advantageous risk-return profile than your portfolio. That can only happen if you dump the EMH though.

OneEyedMan writes:

Insurance (e.g. property and life) is a sort of derivative that reduces risk and is a pretty widely adopted for neither transaction cost nor regulatory arbitrage.

The right standard isn't the fraction of the derivative use that is used to hedge but the fraction of natural risk that can be hedged. For example, oil companies may make up on a small number of the supply of short position in the derivatives markets with speculative and index investors making up the rest. But if before oil companies used to have big exposures to oil prices and now they do not, that would count as a win for hedging.

Kevin writes:

[Comment removed for irrelevance. --Econlib Ed.]

Rohan writes:

@PrometheeFeu, right, that's correct. But your personal rate of return more closely tracks the rate of return of the underlying asset that you really care about. If the Canadian company makes money, your investment in said Canadian company makes money.

I guess the idea here is that your expertise is in selecting good companies, and not predicting exchange rates. So you hedge to get rid of the elements that you have less confidence in. If your expertise is in predicting exchange rates, then you may as well trade currency directly.

But then, I'm not a real expert in this domain. I just program what the finance guys tell me to program.

Doug writes:

Non-linear derivatives, like options, are a way to gain exposure to the second and higher moments of assets. Most evidence seems to indicate that volatility forms another risk factor (like value, small cap and momentum). That is to say those who are willing to hold exposure to volatility are rewarded with positive returns, but hold non-diversifiable risk.

So the question remains why would the typical investor pay a premium to offload his volatility exposure. One theory is that equity drops associated with higher volatility are more indicative or "real world crises" rather than stock market corrections. I.e. volatility rose much more relative to the equity market drops in 2008 than it did in 2000.

In this case an investor is in a better position to take the "pain" of a stock market correction when it's not accompanied by relatively higher spikes in volatility. Most likely he still has his job, his home is holding its value, etc. Whereas an investor would want to have less stock market exposure in periods of deep crisis.

One way to achieve this is by selling volatility, and hence paying willing investors a premium to bear the risk.

Dick White writes:

Many interesting comments and observations. The predicate for the Dr. Kling reader's assumed portfolio was that the risk profile was satisfactory and the question was how does derivatives/hedging increase return holding risk unchanged. The @Doug post identifies one of my biases, namely, the incremental cost of these more expensive assets and the opportunity cost of substituting them for the, say, a portion of an index fund that must be reduced. Finally, how does one determine how much derivative/hedge is enough---again to improve return w/o a change in risk quotient?

Mark V Anderson writes:

Rohan provided a good theoretical example of where hedging makes sense and why. But few ordinary investors would make a hedging bet on Canadian currency to eliminate the exchange risk, because of the additional complications and transaction costs.

However, lots of folks use hedging in real life too, and for exactly the reasons that Rohan states. I've worked in business for the last few decades, and in my experience many multi-nationals hedge the currencies of their foreign subsidiaries in an equal amount to the assets held by these foreign affiliates. In this way, the business is only betting on the overseas business itself, in which management has confidence in its abilities to control, and not on the fluctuating exchange rates, in which management has little expertise.

Of course farmers do this too, selling their crop months before they produce it, so they can eliminate the risk of their crop losing value. Derivatives have a real value in the marketplace, and it relates to lowering risk.

Radford Neal writes:

Mark V Anderson: in my experience many multi-nationals hedge the currencies of their foreign subsidiaries in an equal amount to the assets held by these foreign affiliates. In this way, the business is only betting on the overseas business itself, in which management has confidence in its abilities to control, and not on the fluctuating exchange rates, in which management has little expertise.

Can you tell us which multinationals do this, so we can know not to invest in them? This exposes them to having their foreign investments wiped out by inflationary monetary policy in the foreign country, for the purpose of eliminating "risk" from short-term exchange rate fluctuations that shouldn't actually impact their operations much. The foreign subsidiary can probably continue its operations in the foreign country without being much affected by the exchange rate, just like any other company there. And if the company exchanges products back and forth with its subsidiary, there is no reason why it has to pay attention to the exchange rate in deciding how much product to exchange. There may be some implications with respect to relative labour costs in the different countries, but this seems minor compared to having your entire investment wiped out.

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