## Interest Rates

### Risk for Return

If there is a risk of default, an investor expects to receive a premium in order to protect their investment.

Bond securities are created by a company that is issuing the bond as a form of loan. In essence, the investor is loaning the company money when the investor purchases a bond. Assume that an investor is going to lend $100,000. The borrower already has$1 million in the bank and has always paid back any loans. The investor is reasonably assured that the loan will be paid. Thus, the lender charges a small interest rate. Conversely, if the borrower had no money in the bank and had not repaid loans in the past, then the lender would want a higher return to compensate for the associated risk of default. This investor, like all investors, is risk averse, meaning that the investor expects compensation for increased risk. The danger that the borrower will not repay the loan will earn the investor a default risk premium. Default risk premium is an additional fee that a borrower is charged to compensate for the possibility that the borrower might be unable to pay back the loan.

Because commercial bonds are generated from the debt of the issuing company, they carry a risk of default as well. These types of bonds are rated by their credit in order to help identify the investment risk. The highest grade that a bond can have is AAA. The lowest grades are C and D. A bond with a low rating can be called a junk bond, or a high-yield bond. A high-yield bond is a bond with a low credit rating for which investors can expect a high return on investment. The risk of default is high and the matching default risk premium is also high. The bonds are rated by an outside agency; Moody's and the S&P 500 are two of the most common rating agencies. Because of the risk of default in low-rated bonds, some investor organizations, such as governmental agencies, are forbidden to invest in them.

### How to Calculate Default Risk Premium

The default risk premium can be calculated using the risk-free rate.

Because U.S. Treasury securities, such as Treasury bills, Treasury bonds, and Treasury notes, are assumed to have no default risk, commercial securities are often compared to them by adding the Treasury bond rate to the default risk premium. Default risk is the level of risk investors and lenders may incur if a borrower defaults on a loan. The default risk premium, or the fee a borrower is charged to compensate for the chance they might be unable to pay back the loan, can be calculated by working backward from the risk-free rate. The risk-free interest rate is the expected rate of return with no risks or financial losses, often estimated from U.S. bonds and treasuries. At the risk-free level, Treasury securities and commercial securities will have the same market rate, the rate of interest that a free market can bear.

To calculate the risk-free interest rate, the real rate of interest is added to the inflation premium. The real rate of interest is the rate of interest an investor receives, or expects to receive, after allowing for inflation. The inflation premium is the interest rate that results from lenders compensating for expected inflation. For example, if a 10-year Treasury bond yields two percent, investors would consider two percent to be the risk-free rate of return.
$\text{Risk-Free Interest Rate}=\text{Real Rate of Interest}+\text{Inflation Premium}$
The commercial market interest rate has the same calculation plus the default risk premium, so the default risk premium can be found by subtracting the two. The default risk premium is the amount over and above the rate for Treasury bonds that the investor would like to earn.
$\text{Default Risk Premium}=\text{Market Interest Rate}-\text{Risk-free Interest Rate}$
If the market interest rate for a commercial security is 7 percent and the equivalent risk-free security has a rate of 3 percent, then the default risk premium is 4 percent, or $7\%-3\%=4\%$. To get a real default risk premium, subtract the inflation from this number.

Logic dictates that the default risk premium would be solely calculated based on the bond credit rating of the company. Research has shown this concept is difficult to put into practice. The governance of the issuing company seems to have an effect on the bond credit rating and on the bond yield, but a one-to-one formulaic calculation cannot be made to take advantage of this predictive factor. Likewise, bond ratings seem to be linked to negative stock prices, but increases in stock prices do not seem to increase bond ratings. Again, though this is a predictive factor, it is difficult to use it to calculate a default risk premium.

### Risk-Averse Investors

Investors are assumed to be risk averse and are offered incentives and strategies to balance risk with return.

When an investor is presented with two equally attractive investments, the investor will take the one with the least risk. In this way, investors are risk averse. All of the risk premiums discussed are a response to the natural risk aversion of investors. Risk premiums offer a monetary incentive for taking on the risk associated with the investment. Commercial bonds are often compared to Treasury bonds, government-issued bonds with a maturity date over 10 years, because investors are averse to risk. All things being equal, investors would always take Treasury bonds, so premiums are paid on commercial bonds to make them more attractive.

Risk aversion changes when discussing portfolio investments instead of single-security investments. Portfolios are groupings of investments that balance out the risks associated with any single investment. Portfolios are used to balance risk with return. The risk-aversion coefficient was developed to quantify the investor's risk aversion within a portfolio of investments. This coefficient and the aggregate variance of the portfolio components are used to get an overall utility rating for the portfolio that can be compared to the going rates for risk-free securities.

It is important to note that risk aversion is different from risk tolerance. All rational investors are risk averse, but risk tolerance differs from investor to investor. Risk tolerance is essentially the amount of risk that an investor is willing to take on. For example, younger investors with years of investing ahead of them have a higher tolerance for risk than do older investors. Risk tolerance requires that the investor look at the various forms of risk and identify which are acceptable and which are not.