A bond investor buying a 10-year bond in a CCC rated company may feel more exposed to default risk than a bondholder buying a higher rated bond

Default Spreads on Bonds

The interest rates on bonds are determined by the default risk that investors perceive in the issuer of the bonds. This default risk is often measured with a bond rating and the interest rate that corresponds to the rating is estimated by adding a default spread to the riskless rate. In chapter 4, we examined the process used by rating agencies to rate firms. In this chapter, we consider how to estimate default spreads for a given ratings class and why these spreads may vary over time.

Estimating Default Spreads

The simplest way to estimate default spreads for each ratings class is to find a sampling of bonds within that ratings class and obtain the current market interest rate on these bonds. Why do we need a sampling rather than just one bond? A bond can be misrated or the market can make mistakes with a single bond. Using a sample reduces or eliminates this problem. In obtaining this sample, you should try to focus on the most liquid bonds with as few special features attached to them as possible. Corporate bonds are often illiquid and the interest rates on such bonds may not reflect current market rates. The presence of special features on bonds such as convertibility or callability can affect the pricing of these bonds and consequently the interest rates estimated on them.

Once a sample of bonds within each ratings class has been identified, you need to estimate the interest rate on these bonds. There are two measures that are widely used. The first is the yield on the bond, which is the coupon rate divided by the market price. The second is the yield to maturity on the bond, which is the interest rate that makes the present value of the coupons and face value of the bond equal to the market price. In general, it is the yield to maturity that better measures the market interest rate on the bond.

Having obtained the interest rates on the bonds in the sample, you have two decisions to make. The first relates to weighting. You could compute a simple average of the interest rates of the bonds in the sample or a weighted average, with the weights based upon the trading volume - more liquid bonds will be weighted more than less liquid bonds. The second relates to the index treasury rate since the average interest rate for a ratings class is compared to this rate to arrive at a default spread. In general, the maturity of the treasury should match the average maturity of the corporate bonds chosen to estimate the average interest rate. Thus, the average interest rate for 5-year BBB rated corporate bonds should be compared to the average interest rate for 5-year treasuries to derive the spread for the BBB rated bonds.

While publications like Barrons have historically provided interest rates on at least higher rated bonds (BBB or higher), an increasing number of online services provide the same information today for all rated bonds. The following table is extracted from one such online service in early 2000 for 10-year bonds.

Table 7.6: Default Spreads by Ratings Class - January 2001 (T.Bond rate=5%)

Rating Spread Interest Rate on Debt

Determinants of Default Spreads

Table 7.6 provides default spreads at a point in time, but default spreads not only vary across time but they can vary for bonds with the same rating but different maturities. In this section, we consider how default spreads vary across time and for bonds with varying maturities.

Default Spreads and Bond Maturity

From observation, the default spread for corporate bonds of a given ratings class seems to increase with the maturity of the bond. In Figure 7.2, we present the default spreads estimated for an AAA, BBB and CCC rated bond for maturities ranging from 1 to 10 years in January 2001.

For every rating, the default spread seems to widen for the longer maturities and it widens more for the lower rated bonds. Why might this be? It is entirely possible that default risk is multiplied as we look at longer maturities. A bond investor buying a 10-year bond in a CCC rated company may feel more exposed to default risk than a bondholder buying a higher rated bond.

Default Spreads over Time

The default spreads presented in Table 7.6, after a year of declining markets and a slowing economy, were significantly higher than the default spreads a year prior. This phenomenon is not new. Historically, default spreads for every ratings class have increased during recessions and decreased during economic booms. In Figure 7.3, we graph the spread between 10-year Moodys Baa rated bonds and the 10-year treasury bond rate each year from 1960 to 2000.

The default spreads did increase during periods of low economic growth; note the increase during 1973-74 and 1979-81, in particular. In fact, a regression of default spreads each year against real economic growth that year bears out this conclusion.

Default SpreadBBB-Treasury = 0.47 - 0.04 GNP GrowthReal

After years of high real growth, default spreads tend to shrink.

The practical implication of this phenomenon is that default spreads for bonds have to be re-estimated at regular intervals, especially if the economy shifts from low to high growth or vice versa.

ratings.xls: There is a dataset on the web that summarizes default spreads by bond rating class for the most recent period.

Conclusion

The risk free rate is the starting point for all expected return models. For an asset

to be risk free, it has to be free of both default and reinvestment risk. Using these criteria, the appropriate risk free rate to use to obtain expected returns should be a default-free (government) zero coupon rate that is matched up to when the cash flow or flows that are being discounted occur. In practice, however, it is usually appropriate to match up the duration of the risk free asset to the duration of the cash flows being analyzed. In corporate finance and valuation, this will lead us towards long term government bond rates as risk free rates. It is also important that the risk free rate be consistent with the cash flows being discounted. In particular, the currency in which the risk free rate is denominated and whether it is a real or nominal risk free rate should be determined by the currency in which the cash flows are estimated and whether the estimation is done in real or nominal terms.

The risk premium is a fundamental and critical component in portfolio management, corporate finance and valuation. Given its importance, it is surprising that more attention has not been paid in practical terms to estimation issues. In this paper, we considered the conventional approach to estimating risk premiums, which is to use historical returns on equity and government securities, and evaluated some of its weaknesses. We also examined how to extend this approach to emerging markets, where historical data tends to be both limited and volatile. The alternative to historical premiums is to estimate the equity premium implied by equity prices. This approach does require that we start with a valuation model for equities and estimate the expected growth and cash flows, collectively, on equity investments. It has the advantage of not requiring historical data and reflecting current market perceptions.

3. You have been asked to estimate a riskless rate in Indonesian Rupiah. The Indonesian

government has rupiah denominated bonds outstanding with an interest rate of 17%. S&P has a rating of BB on these bonds, and the typical spread for a BB rated country is 5% over a riskless rate. Estimate the rupiah riskless rate.

4. You are valuing an Indian company in rupees. The current exchange rate is Rs 45 per

dollar and you have been able to obtain a ten-year forward rate of Rs 70 per dollar. If the U.S. treasury bond rate is 5%, estimate the riskless rate in Indian rupees.

5. You are attempting to do a valuation of a Chilean company in real terms. While you

have been unable to get a real riskless rate in Latin America, you know that inflationindex treasury bonds in the United States are yielding 3%. Could you use this as a real riskless rate? Why or why not? What are the alternatives?

6. Assume you have estimated the historical risk premium, based upon 50 years of data,

to be 6%. If the annual standard deviation in stock prices is 30%, estimate the standard error in the risk premium estimate.

7. When you use a historical risk premium as your expected future risk premiums, what

are the assumptions that you are making about investors and markets? Under what conditions would a historical risk premium give you too high a number (to use as an expected premium)?

8. You are trying to estimate a country equity risk premium for Poland. You find that

S&P has assigned an A rating to Poland and that Poland has issued Euro-denominated bonds that yield 7.6% in the market currently. (Germany, an AAA rated country, has Euro-denominated bonds outstanding that yield 5.1%).

a. Estimate the country risk premium, using the default spread on the country

bond as the proxy.

b. If you were told that the standard deviation in the Polish equity market was

25% and that the standard deviation in the Polish Euro bond was 15%, estimate the country risk premium.

a. Estimate the country equity risk premium for Mexico using the equity

standard deviations.

b. Now assume that you are told that Mexico is rated BBB by Standard and

Poors and that it has dollar denominated bonds outstanding that trade at a spread of about 3% above the treasury bond rate. If the standard deviation in these bonds is 24%, estimate the country risk premium for Mexico.

10. The S&P 500 is at 1400. The expected dividends and cash flows, next year, on the

stocks in the index is expected to be 5% of the index. If the expected growth rate in dividends and cash flows over the long term is expected to be 6% and the riskless rate is 5.5%, estimate the implied equity risk premium.

11. The Bovespa (Brazilian equity index) is at 15000. The dividends on the index last

year were 5% of the index value, and analysts expect them to grow 15% a year in real terms for the next 5 years. After the fifth year, the growth is expected to drop to 5% in real terms in perpetuity. If the real riskless rate is 6%, estimate the implied equity risk premium in this market.

12. As stock prices go up, implied equity risk premiums will go down. Is this statement

always true?

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