Financial Strategy Ch. 5

While not a specific homework question, you should be familiar with all of the terms from the Key Bond Terms handout.

KNOW THOSE

Q2) What is the relationship between market rates of interest and bond prices?

Market rates of interest and bond prices have an inverse relationship. When market rates of interest increase, bond prices decline. When market rates of interest decrease, bond prices go up. The reason for this is that the cash flow stream associated with the bond does not change and the market rate of interest represents the discount rate. So, if we discount the same cash flow stream at a higher rate of interest it will be worth less while if we discount it at a lower rate of interest it will be worth more.

Would you ever pay more than $1000 to buy a $1000 non-convertible zero coupon bond? Explain.

No. A non-convertible zero-coupon bond will only pay par value at maturity. There will be no other payments. Therefore, a $1000 par value zero-coupon, non-convertible bond will pay exactly $1000 at maturity. Let's say the bond matures in 4 years. There is never a good reason to pay more than $1000 today to receive $1000 four years later. Even if the market rate of interest was zero, it would make more sense to just hold onto our money rather than pay more than $1000 today to receive $1000 at a later date.

Identify and briefly explain the key determinants of interest rates

1. The real rate of interest 2. Demographics 3. Recent Experiences 4. Culture 5. Expected Inflation 6. Default Risk Premium 7. Maturity Risk Premium 8. Liquidity Risk Premium 9. Special Characteristics Premium

Which bond should have a higher YTM: A) A 20-year bond with a AA rating, or a 20-year bond with a BB rating? B) A 30-year bond with an A rating or a 5-year bond with a BB rating?

A 20-year bond with a BB rating should have a higher YTM than a 20-year bond with a AA rating. The reason for this is that the lower bond rating indicates more default risk. Since the bonds have the same time to maturity, the primary risk differential is default risk. The greater the risk, the higher the YTM should be. B.) There is not enough information to answer this question. The problem is we are changing two important factors - time to maturity and bond rating. The YTM will depend on inflationary expectations (over the 5-year and 30-year periods respectively), maturity risk, and default risk.

Maturity Risk Premium

All else equal, longer term bonds are more sensitive to interest rate changes than shorter risk bonds. Therefore, we typically see a slight risk premium on longer-term bonds due to the greater maturity risk.

Which bond will be the most sensitive (in terms of percentage changes in its price) to interest rate changes?

All else equal, longer term bonds are more sensitive to interest rate changes. Also, all else equal, lower coupon bonds are more sensitive to interest rate changes. Combining these two concepts, the 30-year 0% coupon bond has the longest time to maturity with the lowest coupon rate so should be the most sensitive to interest rate changes.

Choose the correct statement regarding convertible bonds:

Convertible bonds allow investors to change (or convert) the bond into a fixed number of shares of common stock at the bondholders discretion.

Because junk bonds have a higher probability of default than investment-grade bonds, they are a poor investment tool and we should expect to earn lower rates of return on them. True or False? Explain.

FALSE. While it is true that junk bonds have a higher probability of default than investment grade bonds, that does not mean that they are a poor investment or that we should expect low rates of return. The higher probability of default means that they are riskier. Riskier investments should offer higher expected returns to compensate investors for the additional risk (if they were riskier and offered lower expected returns, no one would purchase them). This higher expected returns may make them good investments for some people. Whether or not junk bonds are a good investment depends on the individual. For people with low risk tolerances, junk bonds are likely to be a poor investment (although there could even be some situations where they make sense as part of the overall portfolio for someone with a low risk tolerance as long as they are a very small portion). For people with greater risk tolerance the risk-return tradeoff may be attractive. However, they should always offer higher expected returns than investment grade bonds. Note that higher expected returns do not mean that an investor will earn a higher return. Instead, it means that ON AVERAGE junk bonds will offer higher returns, but that there will be periods where most junk bonds earn low (or negative) returns and in virtually all periods there will be some junk bonds that see large negative returns.

If you thought interest rates were going to decline in the future, you would prefer to buy short-term bonds instead of long-term bonds.

False, you would want the bonds with greater sensitivity -- long-term

If a bond will pay me $1000 upon maturity, why would I ever be willing to pay a premium to purchase it today?

I would be willing to pay a premium for a bond if the cash flow stream that it generates is higher than I can get elsewhere. For instance, if the current market rate of interest is 7%, that implies that newly issued bonds will be paying 7% coupon payments. If I can find a bond with a 9% coupon rate, I will receive an extra $20 per year in coupon payments. If that coupon stream will last for 10 years, then the premium that I am willing to pay is the present value of $20 per year for 10 years.

Recent Experiences

Prior to the financial crisis, savings rates in the US were very low (actually negative). Immediately following the financial crisis, the savings rate temporarily hit almost 9%. Today it is around 5%. When times are good and have been for awhile, people are not concerned with saving for tomorrow. When times are bad (are have recently been so), people have a greater incentive to save for the future.

Identify a situation where short-term bonds may have higher interest rates than long-term bonds

Short-term bonds may have higher interest rates than long-term bonds when inflation is relatively high. The reason for this is that in periods of higher than normal inflation, we should expect it to decline over time (as the Federal Reserve acts to fight the inflation). Thus a shorter-term bond (say 1 year) is likely to see inflation remain high over its remaining life while a longer-term bond (say a 30-year bond) will likely see inflation average a level closer to normal over its life. Therefore, the inflation premium is higher for short-term bonds during periods of higher than normal inflation than it is for longer-term bonds. Remember that the inflation premium is based on average annualized inflation rates that are expected over the entire life of the security

Choose the correct statement regarding the default risk premium. (This is a multiple answer format question which means you should check all that apply...there may be more than one correct response).

The default risk premium will be higher when there is a greater chance for default (the bondholder not getting full coupon/principal payments on time). Treasury bonds are generally assumed to have zero default risk as the Treasury has the ability to print more money. While this general assumption may be getting questioned a little over the last couple years due to higher deficits and overall federal debt, it still appears valid based on the extremely low interest rates on US Treasury bonds. Corporate bonds on the other hand will have a wide range of default risk premiums (largely tied to their bond ratings). Firms with strong bond ratings (AA or AAA) will have extremely low default risk premiums. Firms with weak bond ratings (BB or lower) will have higher default risk premiums.

What is more relevant to an investor A) Yield-to-Maturity or Coupon Rate? B) Yield-to-Maturity or Yield-to-Call?

The Yield-to-Maturity (YTM) is more relevant to an investor than the coupon rate. The coupon rate determines the coupon rate, so it tells us what the cash flow stream looks like, but doesn't take into account what we pay for it. For instance, which would you rather buy...a 3-year 5% coupon bond or a 3-year 10% coupon bond? At first glance, the 10% coupon bond seems better because we will get $100 per year in coupon payments instead of $50. However, how much are we paying for these bonds? What if the 5% bond is selling for $700 and the 10% bond is selling for $1300? We will get a much higher rate of return on the 5% bond making it a better purchase (assuming similar risk levels). Thus, the YTM provides a better measure of what we will earn on a bond because it takes into account more information. Not only does it consider coupon payment, but how much we are paying today and how long we will receive the coupon payment. Another simple way to look at this question is if the coupon rate was a more relevant measure, no one would ever buy a zero coupon bond B.) Sometimes the Yield-to-Maturity (YTM) is more relevant than the Yield-to-Call (YTC) and sometimes the YTC is more relevant than the YTM. It depends on the situation. To understand this, we first must remember what the numbers represent. We defined the YTM as the expected rate of return we would earn on the bond if we bought it today and held it until maturity and the YTC as the expected rate of return if we bought it today and it got called at the first call date. Those definitions come from the viewpoint of the bondholder. However, someone has to pay the bondholder those rates of return and it is the issuer. Therefore, the bondholders expected rate of return is the issuers expected cost. Now, remember who makes the call decision - the issuer. Since the issuer would prefer to face a lower cost, it will likely call the bonds back if the YTC is less than the YTM. Alternatively, if the YTM is less than the YTC, the issuer will not want to call the bond back early. Thus, the investor is likely to receive whichever is lower between the YTM and YTC and that means whichever one is lower is the more relevant number.

How does the length of time until maturity for a bond impact the relationship between market rates of interest and bond prices?

The longer the time to maturity, the more sensitive the bond price will be to changes in the market rate of interest. Long-term bond prices will increase by a greater amount when interest rates go down and will fall by a greater amount when interest rates go up.

Define Special Characteristics Premium

This is a "catch-all" category for other things. Some of the basics are a higher special characteristics premium for callable bonds (as this favors the issuer at the expense of the bondholder), a lower special characteristics premium for convertible bonds (as this provides an extra bonus for the bondholder if the stock does well), and a higher special characteristics premium for bonds paying in different currencies (as this introduces currency risk).

Explain why lower levels of liquidity will result in a higher liquidity premium.

This was addressed earlier as I explained the liquidity premium, but since it is a point upon which many students struggle I thought I'd bring it up in a separate question. Investors prefer liquidity. It is nice to be able to know that even if I bought a 30-year bond, I can exchange that for cash quickly and easily at any time over the 30 years if I decide I no longer want to hold the bond. Alternatively, it is unpleasant to know that if I want to get out of the position before the 30 years is up, it is going to take a long time to sell the bond or I will have to sell it for much less than its true value. Therefore, the greater the liquidity the lower the liquidity premium and the lower the liquidity the greater the liquidity premium.

Assume that company A is issuing two bonds. Bond A is callable and Bond B is non-callable. Everything else about the two bonds is identical. Based on this, we would expect bond B to sell for a higher price than Bond A.

True, because call provisions create a benefit for the issuer (the ability to buy back the bond at a fixed price prior to maturity), investors would prefer to avoid callable bonds and therefore would pay more for a non-callable bond all else equal.

When a bond is trading at a premium ___. (This is a multiple answer format question which means you should check all that apply...there may be more than one correct response).

When a bond is trading at a premium, that means it is trading for more than its par value ($1000). Because you are paying more for the bond today than you will receive at maturity, your net return over the life of the bond (YTM) will be less than the coupon rate.

Culture

a. Some cultures are more geared towards savings while others are more geared toward spending (current consumption). The greater the cultural bias towards saving, the lower the real rate of interest we would expect to see.

Demographics

a. Younger people (under 25) and older people (65+) tend to spend more than their income and have low savings rates (typically either borrowing or spending previous savings). People in-between there are more likely to be saving for retirement. Therefore, the more people in the 25-65 age bracket (relative to those outside it), the greater the supply of savings and lower the real rate of interest.

What is a call provision?

A call provision is a feature in the bond indenture that allows the issuing party to repurchase the bond for a preset price prior to maturity. For instance, a firm may issue a 20-year 8% coupon bond that is callable in 5 years for $1040. Then, if interest rates have declined significantly after five years the firm will find it cheaper to call back the bond rather than to continue paying interest payments for the next 15 years. If they still need additional financing, the will be able to issue new bonds with a lower interest rate. On the other hand, if interest rates go up, the firm will decide not to call back the bond as it would cost them more to refinance it. If they no longer needed the financing, they could buy the bonds back in the open market for less than the call price (since bond prices decline when rates go up.) Note that, everything else equal, call provisions are good for the issuer but bad for the investor. That is because if interest rates go down, the company is likely to call the bond and the investor won't get the full benefit of declining interest rates. On the other hand, if interest rates go up the company is not likely to call which leaves the investor feeling the full downside of increasing interest rates. Because of this, the only way to get investors to buy callable bonds is to pay them slightly more. Therefore, callable bonds will typically offer investors a slightly higher yield in order to offset the call risk.

Expected Inflation

A. Note that the real rate is designed to preserve purchasing power. Therefore, if I expect inflation to average 3% and I want a 1% real return, I need to earn 4% to get the 1% real return. The higher the expected inflation over the life of the investment, the greater the nominal return I need to keep the same real return. It is important to remember that this is not total inflation, but average annualized inflation that is expected over the life. Therefore, during periods of high inflation, the inflation premium may be higher for short-term securities/loans. During periods of low inflation, the inflation premium is likely to be higher for long-term securities/loans.

Liquidity Risk Premium

All else equal, investors want to be able to quickly and cheaply cash out of an investment. This is referred to as liquidity (the ability to sell an asset quickly for fair market value). The longer it takes to sell the bond or the greater the price break we must give the buyer, the less liquid the bond. As investors like liquidity, the accept lower rates of return on bonds (loans) that are highly liquid and demand higher rates of return (a liquidity premium) on bonds (loans) that are less liquid. Therefore, the less liquidity a bond has, the greater the liquidity premium we should expect to see associated with that bond.

Why are bond ratings important?

Bond ratings are important because they provide a measure of the default risk associated with investing in bonds. The worse the bond rating, the greater the default risk. Everything else being equal, investors will demand higher returns (YTMs) for bonds with bad bond ratings. From a firm's perspective, that means a bad bond rating is going to translate into paying more to raise additional debt financing. One important point to remember about bond ratings though is that they only measure DEFAULT risk, and not total risk. There are several other risk factors associated with bonds (such as interest rate risk and liquidity risk) that also must be considered when evaluating the total risk of a particular bond.

What is the three step approach for security valuation and how do I apply it to bond pricing?

The three step approach for security valuation is Forecast all expected cash flows associated with that security over its lifetime Choose an appropriate discount rate Solve for the PV When applying this to bond valuation, we start with step 1. The cash flows associated with a bond are (A) the coupon payments and (B) the par value. The coupon payments are an annuity, paid twice each year. The annual coupon payments are calculated by taking the coupon rate times the par value (which we assume is always $1000). Therefore, a 5% coupon bond will pay $50 coupon payments annually as 5% of $1000 is $50. Since coupon payments are made semi-annually, this will generate a $25 coupon payment every six months. The par value is a single cash flow ($1000) paid at maturity. Next, we must choose an appropriate discount rate. In class, this will be a given. However, it is an important step in practice. The riskier the bond, the higher the discount rate that you must use. Also, as expected inflation increases you will want to increase the discount rate. A common practice is to estimate the discount rate by starting with the interest rate (yield) on Treasury bonds of similar maturity and then adding in a risk premium to reflect how much riskier the bond you are valuing is relative to the Treasury bond. Finally, we solve for PV. This step is easy with bonds. Convert your calculator to 2 Periods per Year. N represents the number of periods (years*2) the bond has remaining until maturity. I/Y represents the discount rate we estimated in step 2. PMT is the coupon payment we calculated in step 1. FV is the par value ($1000). Once we enter these four values into our financial calculator, we then solve for PV.

Which is more sensitive to a change in interest rates, a zero-coupon bond or a 10% coupon bond? Why might this be?

The zero-coupon bond will be more sensitive to changes in interest rates than the 10% coupon bond (in terms of % differences). The reason for this is that the coupon payments start returning some of our investment quicker, so the bond's value is not impacted as much by changes in interest rates. For instance, part of the value of the 10% bond is the $100 in coupon payments during the first year ($50 every ½ year). Since, it is only one year away, its present value will not be changed much by changing the discount rate. However, the zero coupon bond has no coupon payments (the entire cash flow will not be received until maturity which is several years out), so its value will be impacted significantly by changes in the interest rate. Consider the following two bonds Bond A - 10% coupon bond with 10-years remaining and a 10% market rate of interest Bond B - Zero-coupon bond with 10-years remaining and a 10% market rate of interest Calculate the % increase in the bond prices if the market rate of interest drops to 8%. Bond A starting value (at 10%) -- $1000.00 Bond A new value (at 8%) -- $1135.90 Percent Increase -- 13.59% Bond B starting value (at 10%) -- $376.89 Bond B new value (at 8%) -- $456.39 Percent Increase -- 21.09% Calculation for Bond Values Starting Value 10% coupon bond at 10% è No calculation needed, when coupon rate and market rate of interest are the same, the bond price will always be par value ($1000). New Value 10% coupon bond at 8% è 2 P/Y 8 I/Y 20 N 50 PMT 1000 FV PV è $1135.90 Starting Value zero coupon bond at 10% è 2 P/Y 10 I/Y 20 N 0 PMT 1000 FV PV è $376.89 New Value zero coupon bond at 8% è 2 P/Y 8 I/Y 20 N 0 PMT 1000 FV PV è $456.39

Default Risk Premium

Whenever I lend someone money, there is a chance that they will be unable to pay me back the full interest and principal on time. This is referred to as a default. When I evaluate a bond (or make a loan), I need to consider the likelihood of getting paid back my full promised cash flow stream on time. Note that a default does not imply the bondholder (lender) gets nothing. Instead, it is just that the bondholder (lender) does not get the full set of cash flows on time which results in less value to the investor. Typically in the event of a default, the bondholder (lender) will get back at least a portion of the value of the investment. One way to determine the likelihood of default is to look at bond ratings. The lower the rating, the greater the probability of default (and, in turn, the greater the default risk premium). Note that the default risk premium differential between bond rating categories can change over time. In a strong economy, a BB-rated bond may have a 1% higher default risk-premium than an A-rated bond. In a weaker economy, the BB-rated may have a 2% plus higher default risk premium.

Explain the two aspects of the maturity premium (interest rate risk and reinvestment risk).

While the normal situation is for longer-term bonds to be considered risky due to a higher maturity risk premium, this is not as clear-cut as it appears at first glance. We know that bond prices and interest rates are inversely related and that long-term bonds are more sensitive to interest rate changes than short-term bonds. This implies that long-term bonds have more risk. This is true from a price risk perspective. However, there is also a reinvestment risk issue. If I buy a shorter-term bond (say a one-year bond) and have a 10-year investment horizon, I will need to buy 9 additional one-year bonds to get me through the 10-year period. Each time, I will get a different rate of return. If interest rates rise over the 10-year period, my returns will end up being higher than I anticipated based on the current 1-year rate. Alternatively, if interest rates decline over the 10-year period, I will reinvest each time at lower rates and end up worse off than I anticipated. Thus, while longer-term bonds have more price risk, they have less reinvestment rate risk.