Posts Tagged ‘Risk’

Risk-Averse Investors Have Demanded Higher Expected Rates

Posted by admin on June 19th, 2009 | Comments Off

We have assumed that investors are risk-neutral—indifferent between two loans that have the same expected rate of return. As we have already mentioned, in the real world, risk-averse investors would demand and expect to receive a little bit more for the risky loan. Would you rather invest into a bond that is known to pay off 5% (for example, a U.S. government bond), or would you rather invest in a bond that is “merely” expected to pay off 5% (such as my 6.63% bond)? Like most lenders, you are likely to be better off if you know exactly how much you will receive, rather than live with the uncertainty of my situation. Thus, as a risk-averse investor, you would probably ask me not only for the higher promised interest rate of 6.63%, which only gets you to an expected interest rate of 5%, but an even higher promise in order to get you more than 6.63%. For example, you might demand 6.75%, in which case you would expect to earn not just 5%, but a little more. The extra 12 basis points is called a risk premium, and it is an interest component required above and beyond the time premium (i.e., what the U.S. Treasury Department pays for use of money over time) and above and beyond the default premium (i.e., what the promised interest has to be for you to just expect to receive the same rate of return as what the government offers). 

Recapping, we know that 5% is the time-value of money that you can earn in interest from the Treasury. You also know that 1.63% is the extra default premium that I must promise you, a risk-neutral lender, to allow you to expect to earn 5%, given that repayment is not guaranteed. Finally, if you are not risk-neutral but risk-averse, I may have to pay even more than 6.63%, although we do not know exactly how much. 

If you want, you could think of further interest decompositions. It could even be that the time-premium is itself determined by other factors (such as your preference between consuming today and consuming next year, the inflation rate, taxes, or other issues, that we are brushing over). Then there would be a liquidity premium, an extra interest rate that a lender would demand if the bond could not easily be sold—resale is much easier with Treasury bonds.The risk premium itself depends on such strange concepts as the correlation of loan default with the general economy. We can preview the relative importance of these components for you in the context of corporate bonds. The highest-quality bonds are called investment-grade. A typical such bond may promise about 6% per annum, 150 to 200 basis points above the equivalent Treasury. The probability of default would be small—less than 3% in total over a ten-year horizon (0.3% per annum). When an investment-grade bond does default, it still returns about 75% of what it promised. For such bonds, the risk premium would be small—a reasonable estimate would be that only about 10 to 20 basis points of the 200 basis point spread is the risk premium. The quoted interest rate of 6% per annum therefore would reflect first the time premium, then the default premium, and only then a small risk premium. (In fact, the liquidity premium would probably be more important than the risk premium.) For low-quality corporate bonds, however, the risk premium can be important. Ed Altman has been collecting corporate bond statistics since the 1970s. In an average year, about 3.5% to 5.5% of low-grade corporate bonds defaulted. But in recessions, the default rate shot up to 10% per year, and in booms it dropped to 1.5% per year. The average value of a bond after default was only about 40 cents on the dollar, though it was as low 25 cents in recessions and as high as 50 cents in booms. Altman then computes that the most risky corporate bonds promised a spread of about 5%/year above the 10-Year Treasury bond, but ultimately delivered a spread of only about 2.2%/year. 280 points are therefore the default premium. The remaining 220 basis points contain both the liquidity premium and the risk premium—perhaps in roughly equal parts.

Filed under Risk | Tags: ,


Risk Neutrality (and Risk Aversion Preview)

Posted by admin on June 11th, 2009 | Comments Off

Fortunately, the expected value is all that we need to learn about statistics until we will get to Part III (investments). This is because we are assuming—only for learning purposes—that everyone is risk-neutral. Essentially, this means that investors are willing to write or take any fair bet. For example, you would be indifferent between getting $1 for sure, and getting either $0 or $2 with 50% probability. And you would be indifferent between earning 10% from a risk-free bond, and earning either 0% or 20% from a risky bond. You have no preference between investments with equal expected values, no matter how safe or uncertain they may be. If, instead, you were risk-averse—which you probably are in the real world—you would not want to invest in the more risky alternative if both the risky and safe alternative offered the same expected rate of return. You would prefer the safe $1 to the unsafe $0 or $2 investment. You would prefer the 10% risk-free Treasury bond to the unsafe corporate bond that would pay either 0% or 20%. In this case, if I wanted to sell you a risky project or bond, I would have to offer you a higher rate of return as risk compensation. I might have to pay you, say, 5 cents to get you to be willing to accept the project that pays off $0 or $2 if you can instead earn $1. Or, I would have to lower the price of my corporate bond, so that it offers you a higher expected rate of return, say, 1% and 21% instead of 0% and 20%. Would you really worry about a bet for either +$1 or −$1? Probably not. For small bets, you

are probably close to risk-neutral—I may not have to offer even one cent to take this bet. But what about a bet for plus or minus $100? Or for plus and minus $10,000? My guess is that you would be fairly reluctant to accept the latter bet without getting extra compensation. For large bets, you are probably fairly risk-averse—I would have to offer you several hundred dollars to take this bet. However, your own personal risk aversion is not what matters in financial markets. Instead, it is an aggregate risk aversion. For example, if you could share the $10,000 bet with 100 other students in your class, the bet would be only $100 for you. And some of your colleagues may be willing to accept even more risk for less extra money—they may have healthier bank accounts or wealthier parents. If you could lay bets across many investors, the effective risk aversion would therefore be less. And this is exactly how financial markets work: the aggregate risk absorption capability is considerably higher than that of any individual. In effect, financial markets are less risk averse than individuals. 

We will study risk aversion in the investments part of the blog. There, we will also need to define good measures of risk, a subject we can avoid here. But, as always, all tools we learn under the simpler scenario (risk-neutrality) will remain applicable under the more complex scenario (risk-aversion).

Filed under Finance | Tags: ,


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