05 – Default Risk

Junk Bonds

Fallen Angels – bonds that were initially issued as investment grade that were subsequently diminished to junk

Original Issue Junk: bonds issued with low credit ratingLower on the priority scale of firm payments

than “senior debt”

Default-Free Bond Example

Face value = 1000 Price=900 YTM: 1000/900-1 = 11.11% Matures in 1 year

Bond has no chance of default. Guaranteed to get $1000 at maturity.

If you hold the bond to maturity, you earn 11.11% return.

Defaultable Bond

Zero-coupon defaultable bond: Face value: 1000 Matures in 1 yearPrice=$800 YTM: 1000/800-1=25%May default

Suppose investors expect to get only $920 back

Expected YTM = 920/800-1=15%

Default Risk Premium

Default risk premium (DRP) = (YTM defaultable bond)-(YTM default free bond)

In example - DRP=25.00%-11.11%=13.89%

Why is the yield on low-grade bonds higher than that on default-free bonds?

That is, why is the price of the junk bond lower than of the default-free bond?

Default Risk Premium

Prices for low grade bonds are low, in part, because investors don’t expect to get all promised payments.

1000

900

11.11%

Default-Free Bond1000

Defaultable Bond

920

800

25%

15%

Investors expect to get only 920 in payments.They expect to earn a yieldof 15% YTM is always calculated

using promised payments.

Expected Yield

YTM: calculated using promised payments. Expected YTM: calculated using expected

payments.

In example, if YTM of the junk bond was 11.11%, price would be 900 and investors would expect to get a yield of only 920/900-1=2.22%

Any reasonable investor should not hold low-grade bonds unless the expected yield is at least as high as that on default-free bonds.

Expected Yield

Why is expected yield on low-grade bonds higher than on default-free bonds?

1000

900

11.11%

Default-Free Bond1000

Defaultable Bond

920

828.08

11.11%

Why isn’t the price of the lowgrade bond 828.08? At thisprice, the expected yield fromthe low-grade bond is thesame as on the default-freebond.

20.8%YTM

That is, why isn’t the price of the low-grade bond 828.08?

Expected Yield

Why is expected YTM on junk bonds higher?

Because of the uncertainty regarding promised payments. In example, the 920 expected payment is only a

guess. In reality, the firm could end up paying a lot more or a lot less.

Expected Yield

In general, riskier financial assets are priced so that, on average they are expected to give higher returns.Small Stock vs. Large Stocks

Any kind of uncertainty that causes returns, on average, to be higher is called systematic risk.

Default Risk

Systematic Default Risk: The uncertainty surrounding payments investors will actually receive on a low-grade bond.

Because of systematic default risk, the expected (average) yield on low grade bonds is higher than the yield on default-free bonds.

Systematic Default Risk Premium

Systematic Default risk premium = (Expected YTM defaultable bond)-(YTM default free bond)

In example, SDRP=15.00%-11.11% = 3.89%

This spread is determined by The level of uncertainty How investors feel about this uncertainty

Systematic Default Risk Premium

Comparing across bonds, as uncertainty surrounding the expected payments increases SDRP increases.

Across time, as investors feel “more queasy” about bearing this risk, SDRP increases for all bonds.

Bond Yields

Yields and Financial Crises The default risk premium increases substantially during

times of financial crises. Why?

1) Greater probability of defaultInvestors expect to get less, and accordingly, prices drop.

2) There is greater uncertainty surrounding the expected payments.The systematic default risk premium increases leading to further drop in price and an even greater default risk premium.

3) Flight to qualityDuring crises, investors flee to the safety of default free bonds, causing the yields of such bonds to decrease leading to an even greater default risk premium.

Yields and Financial Crises

Illustration of points 1, 2, and 3 from previous slide

1000

900

11.11%

Default-Free Bond1000

Defaultable Bond

920

800

25%

15%

DRP=25-11.11=13.89

Yields and Financial Crises

Illustration of points 1, 2, and 3 from previous slide

1000

Default-Free Bond1000

Defaultable Bond

850

730

Expected payment dropsdue to higher probability ofdefault (point 1)

Systematic default riskpremium increases dueto greater uncertainty(point 2)

16.4%

37%920

8.7%

Relative riskof default freebonds drops.Demand curveShifts right.Yields decrease(point 3)

DRP=37-8.7=28.3

Source: Altman, “Defaulted Bond and Bank Loan Markets and Outlook” (2004)

Example

YTM on default-free bond: 8% YTM on junk bond: 33.33% Expected YTM on junk bond: 12%

Assuming these are both zero-coupon bonds that mature in 1 year, what is expected payment on junk?

Example.333=1000/price-1Price=1000/1.333=750E[payment]/750-1=0.12E[payment]=750*1.12=840

Suppose financial distress strikes and the market expects the junk bond to pay only 600 at year-end. Accordingly, the price drops to 530.

What is YTM? What is E[YTM]?

Example

YTM of junk bond is 1000/530-1=87% Expected YTM = 600/530-1=13.21%

What is the default risk premium before and after the financial crisis hit? Assume the crises caused the YTM of the default-free bond to fall to 7%. Before: 33.33% - 8.00% = 25.33 After: 87%-7% = 80%

Example

What is the difference in expected yields before and after the crisis? Assume the crises caused the YTM of the default-free bond to fall to 7%.Before: 12%-8%=4%After: 13.21%-7%=5.21%