## Introduction

Market risk is the risk that the value of a tradable asset will lose in value due to market factors. For instance, stocks can drop or rise in value, interest rates can change, affecting the prices of bonds. Market risk is not very subtle - one can usually see in real-time how much money is made or lost. It is likely the first thing to come to a person's mind when he is quizzed about the risks of investing. Because it is so obvious and ubiquitous, a lot of time and effort has been spent to model, understand and contain market risk. The subject is far too large to cover in one node. In order to give a good example of how to measure market risk, the Sharpe Ratio will be presented. I will then discuss some techniques to hedge it.

## Sharpe ratio1

The Sharpe ratio is in essence a measure of the return we get divided by the risk we need to take for this. Here, risk usually means market risk.

Let us start with the definition of return. We note that there exist certain risk-free investments, most notably government bonds in a credit-worthy government. Now, in essence, anyone can get this type of return without taking any risk, so this return is the baseline. The excess return is the expected return on the investment, say 6%, minus the return on a risk-free investment, say 2%. Hence, the excess return in this example is 4%

The risk can be measured by estimating the standard deviation of the historical returns. Of course, this assumes our estimated return is approximately normally distributed and that our historical returns are a good estimate for the future returns. Let's assume our hypothetical asset has around 10% annual fluctuations in return. This would put the Share ratio at around 0.4. Ref. 1 suggests this is a pretty normal Sharpe ratio. It also means that when investing around 3 years, we have a pretty good chance of being up.

In the discussion on risk, I've already mentioned there are some assumptions made in computing the Share partio. These assumptions are usually false. This makes the Sharpe ratio is a pretty crude tool to measure the risk/return. However, it can be useful in attempting to minimize market risk. By investing in products with a good Sharpe ratio, we can get more return with less risk, at least, in theory.

## Minimizing market risk

There are a few common techniques to minimize market risk. I'll sum up a few of them here.

• Diversification: Perhaps the most old-fashioned way of minimizing risks, the theory is that your risk becomes smaller as you spread your money over multiple assets classes. Statistically, this is true - if you split your money over, say, 10 different stocks instead of 1, your fluctuations are expected to be less - by a factor of sqrt 10, to be exact, if all stocks have the same volatility and no correlation. In pratice, stocks are usually correlated, so the risk reduction is a lot less than that factor. Furthermore, this tends to work reasonably well until the shit really hits the fan, because in such cases, everything tends to go down together.
• Market-neutral portfolio: This one is popular with hedge fund. Imagine we think that, say, oil stocks will outperform. We can then go long oil stocks and go short the index as a hedge. This way, I'm hedged when the whole market crashes. This puts a lot of faith in my initial assessment that oil stocks will go up: if I'm wrong, the long-term tendency of stocks to trend up won't help me.
• Option strategies: Options can be used to create as interesting a risk profile as you want, with corresponding returns. This also means there are many interesting ways to blow up. Nonetheless, buying a crash put under a portfolio, perhaps compensated by selling calls, is a popular if a bit expensive way of hedging against the worst market tantrums.

## Conclusion

Given the techniques above, market risk can be taken in exactly the way a market participant wants to have it. This means that smart investors can easily make sure they don't take more market risk than they want to bear. This makes market risk a risk that is, in practice, normally not extremely dangerous, no matter how painful a stock market crash might look. In practice, the much more difficult to predict but potentially far more devastating liquidity risk and counterparty risk should never be underestimated. As an example, losing 10% on your structured product because the market crashes is one thing. Losing the other 90% because it was guaranteed by Lehman Brothers is far, far worse, especially if you needed that 90%.

## Source

1. http://en.wikipedia.org/wiki/Sharpe_ratio

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