# Credit risk: At what price?

When you suffer the credit risk that a borrower might not repay a loan, what is the premium - the higher interest rate - that you should charge him?

Suppose the riskless interest rate is 10%. Suppose I borrow Rs.100 from you, promising to repay the loan next year. What is the interest rate that I should be charged? If I am the government, you would want me to repay Rs.110 to you next year (an interest rate of 10%).

But I am not the government. Suppose I have a 1% probability of defaulting, i.e. of your getting nothing from me next year. What should you demand from me next year in compensation for this risk?

It turns out that Rs.111.11 with 99% probability, or Rs.0 with 1% probability, averages out to Rs.110. So you might say: I am to pay you Rs.111.11 in repayment of the loan (i.e. an interest rate of 11.11%).

This is a role that credit rating agencies can play. A good credit rating is supposed to be a good forecast of the failure probability of a corporate bond. (A bad credit rating gives you an incorrect estimate of the failure probability). Credit rating agencies should put out clear tables showing the failure probability for each rating category on a required horizon, and showing the performance of their ratings in the past. It should be possible to know that a BBB+ bond fails with probability 0.1%, etc. India's credit rating agencies have yet to persuade us that their ratings are clearly associated with well understood failure probabilities. However, once this is known, you can combine the riskless rate (10%) with the estimated failure probability (1%) to come up with a required rate of return (11.11%).

Is this a fair calculation? Emphatically not! You are bearing risk by taking a chance that you lose your money, and yet (on average) you are only getting the 10% that you get on government securities. In this case, you would be better off simply owning government securities! Why would you bear this risk if (on average) it only gives you the return of government securities?

In the specialised jargon of economics, you would only be willing to accept a return of 11.11% if you are risk neutral, i.e. the uncertainty does not bother you at all; you only care about the average return. Most of us are not risk neutral.

In return for bearing this risk, you must demand a risk premium, a higher return that compensates you for this risk. If I did not offer you a risk premium (i.e. I only offered you a return of 11.11%), you would just ignore me and buy government bonds.

Hence, the analysis of a corporate bond based on its credit rating is fundamentally incomplete. The best information that a credit rating can give is an estimate of the failure probability. A good credit rating can tell you that a bond X will default with probability 1%. When the GOI interest rate is 10%, this tells us that the minimum return that the bond must pay, in order to be competitive, is 11.11%. But it does not tell us the full story: the risk premium remains.

This is where matters become a little complicated. Your quest for a risk premium cannot be discussed at the level of a single corporate bond. It has to be in the context of your full portfolio. For example, suppose you have two financial products X and Y, where Y fares well when X does badly, and vice versa. In this case, the fluctuations of the two cancel out, and you don't bear any risk from having them (in combination) in your portfolio. In this case, you would not demand a risk premium.

The basic principle of finance is that risk premia should be calculated in these steps:

• Assume that an investor has a very well diversified portfolio.
• Assume that he adds a small amount of product X into this portfolio.
• What is the incremental risk into the portfolio caused by X?
• The risk premium for owning X should be proportional to this incremental risk.

This idea is standard in the analysis of equities. The risk premium for a stock is not proportional to its own volatility. Instead, the risk premium for a stock depends on what risk it adds into a well diversified portfolio (i.e. its beta). We demand a risk premium for the correlation between a stock and Nifty; not for the volatility of the stock alone. The risk premium for a stock cannot be judged by doing security analysis, it has to be judged by doing portfolio analysis.

The same idea holds for corporate bond analysis. We cannot talk about the risk premium for a given bond by doing security analysis; we need to do portfolio analysis. Consider a well diversified portfolio of bonds and equities. Now imagine adding a bond X into this portfolio. What is the incremental risk caused by X? This incremental risk should drive the risk premium.

Hence, the risk premium for a corporate bond roughly depends on the extent to which the failure of this bond is correlated with Nifty. A bond X where default occurs "at random", regardless of whether Nifty is doing well or badly, is one which does not require much of a risk premium. In fact, the risk of bond X can be eliminated through diversification. A bond Y where default is likely when Nifty does badly, and unlikely when Nifty does well, is one which requires a higher risk premium.

These issues are subtle and only partly understood. The analysis of diversification and risk premia for equities was well understood by 1964. In contrast, researchers have only started coming to grips with understanding portfolios of corporate bonds and their risk premia in the late 1990s.

The corporate bond market in India is ripe for takeoff, with the onset of depository settlement for corporate bonds and the access to a well defined zero coupon yield curve on government securities. The zero coupon curve is the foundation for analysing corporate bonds; every corporate bond should be priced by adding credit premiums on top the zero coupon yield curve. However, forming portfolios of corporate bonds now requires new heights of sophistication: (a) In demanding and exploiting clear default probabilities from credit rating agencies, and (b) In understanding correlations in the default process for estimating risk premia.

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