1. 9. Other Risks and the Value of Cash Flows
Aside from Interest Rate Risk, there are 4 other risks that institutions consider when developing their portfolio.
Not considering the risks could result in unwanted exposure and result in the financial instability or worse, bankruptcy.
Problem facing most institutions is that the risks are difficult to measure.
1. Default Risk
2. Illiquid Assets
3. Tax
4. Prepayment or embedded options in cash flows

2. 9.1 Default Risk
Default Risk — the chance that a borrower will not be able to make promised payments.
Counterparty Risk-- the possibility of default in one firm will cause defaults in other firms/institutions holding its assets. This will depend on the exposure of an institution to one type of firm as well as the probability of default.
The difference in promised interest rates between otherwise identical securities (differing only in risk) is known as credit spread. For example, a lower rated bond such as a BBB has higher yields than a AAA bond with the same cash flows.

3. 9.2 Measuring Default Risk: Analysts’ Assessments
Operating leverage refers to the cost structure of a business and the degree to which fixed costs vs. variable costs dominate a firm.
Higher fixed costs imply the firm is more susceptible to fluctuations in revenues.
A measure of a firm’s debt vs. equity is known as financial leverage.
Higher debt/equity ratio implies the firm is more susceptible to fluctuations in earnings.
Credit Rating Agencies
Four firms: Moody’s, Standard & Poor’s, Duff & Phelps, Fitch
Evaluate default risk of firms and rank. Investment grade, speculative grade, high-yield or junk bonds.

4. 9.3 Measuring Default Risk: Market-Based Measures
Credit risk is measured by the market through prices and yield differentials.
Another measure is the ratio of a security’s price to that of a default-free synthetic Treasury security (having the same cash flows).
A simple model with zero-coupon bonds:
F: Face Value
DF: Default Face Value
PR: Price of Risky Corporate Debt
PT: Price of Synthetic Treasury

5. 9.4 Measuring Default Risk: Problems with Market-Based Measures
Why is it practically difficult to determine default probabilities from yields and prices?
Difficult to make a synthetic T-bill, especially since bonds are usually coupon bearing rather than zero-coupon bonds.
Uncertainty about when exactly prepayment or call options will be exercised. Therefore, it is difficult to price the bond even if there is no default.
The amount recoverable from a bond, DF, is usually not easy to determine before the bond is in default.
People’s risk aversion and market sentiments may incorrectly price the default risk.

6. 9.5 Measuring Default Risk: Using Historical Data
One can look at which bonds have defaulted in the past and try to estimate the probabilities of default for the different ranked bonds.
Data is almost impossible to get. Many institutions have the data from historical relationships with customers.
In times of crisis, historical information may not be a very good indicator of future performance. Spreads tend to change with market uncertainty.
Because default is a rare event, it is difficult to estimate. (Tail problems)
The default probabilities often depend on the horizon you intend to hold the asset. A longer horizon often means there is a larger chance of default and it also means the estimate of the default is more difficult to interpret because of uncertainties in the future.
You are also interested in whether there was an event that lead to or contributed to the default. Default probabilities may change under certain macroeconomic conditions.

7. 9.6 Measuring Default Risk: Breakeven Default Rates
The breakeven default rate is the percentage of the value of outstanding risky debt that must default in order to equalize expected returns.
Example. What is the breakeven default rate of the risky bond with respect to the riskless bond?
What happens to the breakeven default rate as the maturity of the two bonds increases? What would happen if the risky bond had a YTM of 11%?

8. 9.7 Measuring Default Risk: Zero-Coupon Curve
Plots difference in yields of risky bond less a ZCB Treasury bond against maturity.
The longer the maturity of the bond, the larger the spread.
Why can’t they use coupon bonds to calculate the spreads?
Spread (bp)
BBB
AAA
Maturity (yrs)

9. 9.7 Measuring Default Risk: Par-Spread Curves
Only plots YTM on bonds selling close to face value (par).
Par-spread is defined as the difference in yield that would make the risky bond sell at face value
More difficult to interpret because it is not clear what close to par implies. There could be lots of reasons why the bond is not selling at par which have nothing to do with the credit spread. Also, the spreads only cover a select number of bonds.
Par-Spread (bp)
BBB
AAA
Maturity (yrs)

10. 9.8 Illiquidity Risk
A liquid financial instrument can be converted to cash quickly, in sizable volume, without influencing the price appreciably.
One indication of high liquidity is a narrow bid-ask spread.
The relation between bid-ask spreads and more actively traded (short-term assets) is not one-to-one. One would expect bid-ask to increase for less actively traded securities but that is not always the case.
Bid-ask spreads tend to be larger on longer maturity and higher risk assets
The most liquid of Treasury bonds are those that were recently issued — “On-the-run bonds.”
The larger problem comes in estimating the illiquidity risk of holding a portfolio of loans where there is no defined market for loans. When banks or institutions run into difficult, they often have to sell-off their assets quickly at reduced prices “hair-cuts” because they are illiquid.

11. 9.9 Tax Risk
Debt instruments of state and local governments are referred to as Munis.
Munis are exempt from federal taxation on interest income. In the US, debt issued by state and municipals governments are not taxed the same as the US government.
If the applicable tax rate is T, then the yield of a tax exempt bond should be YT x (1-T) (controlling for other risks, and YT is the taxable yield).
In Canada, instruments such as RRSP that offer a tax rebate to investors would also have a lower yield than their tax bearing counterparts.

12. 9.10 Uncertainty of Cash Flows
Cash flows are often not deterministic.
Prepayment on Mortgages (Mortgage-Backed Securities) is not predetermined
Uncertain when people will pay-off loans.
Callable bonds.
Securities with uncertain cash flows must also have higher yields.
This extra yield is referred to as option adjusted spread (OAS).
OAS declines as the volatility assumption increases. This is because the investor is willing to accept a lower yield (as volatility increases) in return for the prepayment option.

13. 9.12 Estimating prices with OAS
Suppose the annual OAS spread on a mortgage is 50bp. If the homeowner pays 10% annually on a $100,000 3 yr loan, what is the value of these cash flows on the bank’s balance sheet if the homeowner is likely to repay once interest rates fall below 7.75%. Suppose interest rates are expected to follow these paths over the next three years with a 60% chance of moving up and a 40% chance of moving down.
14.96%
11.41% 8%
10.23%
7.65% 7%

14. 9.13 Summary
We discussed four types of risk, and their tools of detection, which affect the yield of a financial instrument:
Default risk - agency ratings, market based measures of default, breakeven default rates, and zero and par spread curves
Liquidity risk - bid-ask spreads and trading volume
Tax treatment - tax adjustments
Cash flow sensitivity - option- adjusted spreads
Any, or all of these may be present in a financial instrument along with interest rate risk discussed in earlier sections.