11. Bonds

Question 1

What is the coupon rate?

Answer 1

First, let’s back up and start with coupon %. This is the stated percent that a bond pays. It generally does not change or fluctuate over the life of a bond. Thus, a 30-year bond when it’s issued might have a stated coupon of 5%. That means that it pays $50 for ever $1,000 invested. If you hold the bond for 30 years, you will receive the $50 every year regardless of interest rates or market conditions (unless the bond defaults or is called).

Question 2

What is the current yield?

Answer 2

Now, let’s take that same $1,000 bond and let’s assume that interest rates rise so that an investor can get a similar bond with a 6% yield. If you tried to sell your 5% bond for $1,000 an investor would be foolish to buy it when they can get a bond that pays 6% for $1,000. So, in order to sell the bond, you’ll have to give a discount on the price. Say you offer to sell your bond for $800. The bond still pays $50 per year so that means that the current rate is now $50/$800 or 6.25%. The investor would now be wise to purchase your bond at a current yield of 6.25% versus the other bond at 6%. Of course, to sell the bond, you had to lose $200 via the discount you provided. That’s why rising interest rates are bad for holders of bonds. The opposite is also true. Falling interest rates make the value of bond greater because investors will pay more to get high yield bonds.

Question 3

What is the yield to maturity?

Answer 3

Yield to maturity is the most complicated of the yield terms but it also the one investors use the most. It includes not only today’s payments, but all future payments and assumes that those payments are reinvested at the same rate. It also includes the repayment of principal. If you bought a discounted bond for $800 but it’s par value is $1,000 then you’ll receive that extra $200 at maturity. In general, if you’ve purchased a bond at a discount, then the yield to maturity will be greater than the current yield because of this. If you purchased the bond at a premium, then the opposite is true.

Question 4

What is the relationship between YTM, coupon rates, and current yield for bonds trading at a premium or discount?

Answer 4

Discount:
YTM > c
YTM > CY

Premium:
YTM < c
YTM < CY

Question 5

You have a 8 percent note maturing in five years trading at 80. What is the current yield to maturity?

Answer 5

Simple Method:

YTM = [Coupon Payment + (Discount/T)] / Average Price
YTM = [8 + (20/5)] / 90 = 13.3%

20 / 80 = 25% / 5 = 5% + 8 / 80 = 15% minus compounding = ~14%.

Complex Method:
YTM = 0.5[(Annualized Capital Gain + Coupon)/Bond Price + (Annualized Capital Gain + Coupon)/(Par - Annualized Capital Gain)]

Annualized Capital Gain = (Par - Bond Price) / T

YTM = 0.5[(4+8)/80 + (4+8)/(100-4)]
YTM = 0.5[(12/80) + (12/96)]
YTM = 0.5[(3/20) + (1/8)]
YTM = 13.75%

Question 6

Suppose you buy a $1000 bond at par value with 5% coupon rate maturing in five years. The market price for the bond is $900. What is the CY and the YTM?

Answer 6

Simple Method:
YTM = [Coupon Payment + (Discount/T)] / Average Price
YTM = [50 + (100/5)] / 950 = 7.37%

Complex Method:
YTM = 0.5[(Annualized Capital Gain + Coupon)/Bond Price + (Annualized Capital Gain + Coupon)/(Par - Annualized Capital Gain)]

Annualized Capital Gain = (Par - Bond Price) / T

YTM = 0.5[(20 + 50)/900 + (20 + 50)/(1000 – 20)] 
YTM = 0.5[(7/90) + (7/98)]
YTM = 0.5(0.0778 + 0.0714) = 7.46%

Question 7

What is the 1-year holding period return of a 30 year US Treasury if it is currently selling at par ($100) with a 7% coupon and the YTM a year from now is 11%.

Answer 7

(1) Find the Price of the Bond at t=1
We know Price and Yield have an inverse relationship, therefore intuitively the price should be lower at t=1 since yield increased to 11% (since its selling at par, current YTM is 7%).

Use current yield formula in order to estimate.
CY= C/P
11%=7/P
P= 63.6
Remember for discount bonds CY is greater than YTM and for premium bonds CY is less than YTM.

(2) Now we can solve for Holding Period Yield = (Ending Value – Beginning Value + Coupon Payment)/Beginning Value
HPY = (65.40-100 + 7)/100 = -27.6%

Question 8

Given negative news about a company, what happens to the pricing of the equity versus the senior debt?

Answer 8

Since equity is riskier and there is more uncertainty associated with it, the equity will be more volatile and decline in price by a greater percentage than the debt.

Question 9

The current one year interest spot rate is 5.2 percent and the six-month interest spot rate is 5.4 percent. What is the implied forward rate for the second half of the year?

Answer 9

The rate over the first six months and second half of the year must average out to give 5.2 percent for the full year. So 5.2 percent = (5.4 percent + unknown forward rate)/2, which solves to 5.0 percent. The spot rate is the price that is to be paid immediately (settles in one to two business days). In contrast, forward rates are the projected spot rates, which can fluctuate based on the market. Basically, buying a forward means you’re locking in a price now for future settlement, though the true spot rate that settles then may be different.

Question 10

Define the difference between the “yield” and the “rate of return” on a bond?

Answer 10

The “yield” on a bond is the return you earn if you hold the bond to maturity versus the rate of return is the actual realized return to the bond holder. So, if the bond is sold before maturity, the rate of return can be higher or lower than the yield. A bond may have a promised yield of 5 percent, but you bought this before the economic crisis, so interest rates have dramatically fallen. This increases your rate of your return if you sell now; if you hold to maturity then your yield and return will be the expected 5 percent.

Question 11

What is duration?

Answer 11

Very simply put, duration is the measure of sensitivity of a bond’s price to changes in interest rates. Duration is measured in years. Typically, the longer the bond issuance, the more sensitivity (as there are more cash flows in later periods) to interest rates, and the higher the duration. Therefore, the lower the duration that a bond has, the less volatility and sensitivity to interest rates it will have.

Question 12

What is convexity?

Answer 12

As duration is the measure of sensitivity of a bond’s price to changes in interest rates, convexity is the measure of sensitivity of a bond’s duration to changes in interest rates. In essence, duration could be considered the first derivative of a bond’s interest rate sensitivity and convexity the second.

Question 13

Let’s say a report released today showed that inflation last month was very low. However, bond prices closed lower. Why might this happen?

Answer 13

Bond prices are based on expectations of future inflation. In this case, you can assume that traders expect future inflation to be higher (regardless of the report on last month’s inflation figures) and therefore they bid bond prices down today. (A report which showed that inflation last month was benign would benefit bond prices only to the extent that traders believed it was an indication of low future inflation as well.)

Question 14

If the price of the 10-year Treasury note rises, does the note’s yield rise, fall or stay the same?

Answer 14

Bond yields move in the opposite direction of bond prices. Therefore, if the price of a 10-year note rises, its yield will fall.

Question 15

If you believe interest rates will fall, should you buy bonds or sell bonds?

Answer 15

Since bond prices rise when interest rates fall, you should buy bonds.

Question 16

What major factors affect the yield on a corporate bond?

Answer 16

The prices of corporate bonds fluctuate as they are traded on the bond market. Like government bonds, a corporate bond pays a fixed amount of interest each year, which is called the coupon rate. If bond prices fall, the effective interest rate (called the yield) goes up because an investor pays less but gets the same coupon rate. Conversely, if the bond price increases, the percentage yield goes down.

(1) Prevailing rates – Corporate bonds compete in the market for investor dollars. If prevailing interest rates should rise, the yields bonds provide at a given price become less attractive. Demand for the bonds falls, creating downward pressure on prices. Bond prices tend to decline with the effective interest rate climbing until it is competitive with new interest rate levels.
(2) Credit risk – Next to prevailing interest rates, the most important factor affecting the interest rates of corporate bonds is credit risk. Corporate bonds are assessed based on the probability a company will be able to redeem (pay off) the bonds at maturity. Most investors rely on bond rating services to provide credit risk ratings. The bonds of companies with the best credit ratings (typically designated AAA) pay lower interest rates as a rule because investors will accept lower yields in return for reduced risk. If a company’s bond ratings are downgraded, the price of the bonds usually falls, resulting in increased yields. This occurs because investors want better interest rates to compensate for the increased risk.

(3) Other factors – anything that influences risk
- Callable – In financial markets, uncertainty about the future means increased risk. As with credit risk, uncertainty regarding bonds tends to result in lower prices and higher yields. Some corporate bonds are callable; This means the company can decide to redeem the bonds early, possibly causing investors to lose out on above-average yields.
- Long Maturities – Bonds with long maturities also carry more risk since conditions years in the future are more uncertain than in the short term. In either case, investors generally demand higher interest rates to offset the increased risk these bonds carry.

Question 17

If a bond’s coupon rate is 7% and the expected return in the market is 5%, is the bond priced at a premium or a discount?

Answer 17

The bond is priced at a premium.

For example, if a bond has a 7% coupon at a time when the prevailing interest rate is 5%, investors will “bid up” the price of the bond until its yield to maturity is in line with the market interest rate of 5%. As a result of this bidding up process, the bond will trade at a premium to its par value. A bond premium will reduce the yield to maturity of the bond, while a bond discount will enhance its yield. The size of the premium will decline as the bond approaches maturity. The premium will dwindle to zero at maturity, since bond issues are generally redeemed at par.

Question 18

If unemployment is low, what happens to inflation, interest rates, and bond prices?

Answer 18

If unemployment is low, the economy is doing well, which means consumers are spending more money. Inflation rises along with interest rates, which causes bond prices to fall

Question 19

If the stock market falls, what would you expect to happen to bond prices, and interest rates?

Answer 19

If the stock market falls, investors turn to other investment vehicles in pursuit of yield, such as bonds. This increase in demand will drive up the prices of bonds, and as a result, lower interest rates.

Question 20

If interest rates rise by 1%, what would happen to stock prices? Why?

Answer 20

A stock’s required rate of return is made up of two parts: the risk-free rate and the risk premium. As the government adjusts key interest rates, the risk-free rate will change. If the government raises rates, the risk-free rate will rise also. If nothing else changes, the stock’s target price should drop because the required return is higher. The reverse is true. If interest rates fall, then the stock’s target price should rise because the required return has dropped.

Question 21

Given such a change in interest rates, what will happen to bond prices?

Answer 21

An increase in interest rates would cause bond prices to fall.

Question 22

How are bonds priced?

Answer 22

Bonds are priced based on the net present value of all future cash flows expected from the bond.

Question 23

How would you value a perpetual bond that pays you $1,000 a year in coupons?

Answer 23

Divide the coupon by the current interest rate. For example, a corporate bond with an interest rate of 10% that pays $1,000 a year in coupons would be worth $10,000.

Question 24

When should a company issue debt instead of issuing equity?

Answer 24

First, a company needs a steady cash flow before it can consider issuing debt (otherwise, it can quickly fall behind interest payments and eventually see its assets seized). Once a company can issue debt, it will do so for a couple of main reasons.

If the expected return on equity is higher than the expected return on debt, a company will issue debt. For example, say a company believes that projects completed with the $1 million raised through either an equity or debt offering will increase its market value from $4 million to $10 million. It also knows that the same amount could be raised by issuing a $1 million bond that requires $300,000 in interest payments over its life. If the company issues equity, it will have to sell 20% of the company ($1 million / $4 million). This would then grow to 20% of $10 million, or $2 million. Thus, issuing the equity will cost the company $1 million ($2 million - $1 million). The debt, on the other hand, will only cost $300,000. The company will therefore choose to issue debt in this case, as the debt is “cheaper” than the equity.

Also, interest payments on bonds are tax deductible. A company may also wish to issue debt if it has taxable income and can benefit from tax shields.

Question 25

What major factors affect the yield on a corporate bond?

Answer 25

The short answer: (1) interest rates on comparable U.S. Treasury bonds, and (2) the company’s credit risk. A more elaborate answer would include a discussion of the fact that corporate bond yields trade at a premium, or “spread,” over the interest rate on comparable U.S. Treasury bonds. (For example, a five-year corporate bond that trades at a premium of 0.5%, or “50 basis points,” over the five-year Treasury note is priced at “50 over.”) How large this “spread” is depends on the company’s credit risk: the riskier the company, the higher the interest rate the company must pay to convince investors to lend it money and, therefore, the wider the spread over U.S. Treasuries.

Question 26

If you believe interest rates will fall, which should you buy: a 10-year coupon bond or a 10-year zero coupon bond?

Answer 26

The 10-year zero coupon bond. A zero coupon bond is more sensitive to changes in interest rates than an equivalent coupon bond, so its price will increase more if interest rates fall.

Question 27

Which is riskier: a 30-year coupon bond or a 30-year zero coupon bond?

Answer 27

A 30-year zero coupon bond. Here’s why: A coupon bond pays interest semi-annually, then pays the principal when the bond matures (after 30 years, in this case). A zero coupon bond pays no interest, but pays one lump sum upon maturity (after 30 years, in this case). The coupon bond is less risky because you receive some of your money back before over time, whereas with a zero coupon bond you must wait 30 years to receive any money back. (Another answer: The zero coupon bond is more risky because its price is more sensitive to changes in interest rates.)

Question 28

What is The Long Bond trading at?

Answer 28

30 year = 2.87%
20 Year = 2.50%
10 Year = 1.72%

The Long Bond is the U.S. Treasury’s 30-year bond. In particular for sales & trading positions, but also for corporate finance positions, interviewers want to see that you’re interested in the financial markets and follow them daily.

Question 29

If the price of the 10-year Treasury note rises, does the note’s yield rise, fall or stay the same?

Answer 29

Bond yields move in the opposite direction of bond prices. Therefore, if the price of a 10-year note rises, its yield will fall.

Question 30

If you believe interest rates will fall, should you buy bonds or sell bonds?

Answer 30

Since bond prices rise when interest rates fall, you should buy bonds. 10. How many “basis points” equal ? percent?
Bond yields are measured in “basis points,” which are 1/100 of 1%. 1% = 100 basis points. Therefore, ? percent = 50 basis points.

Question 31

Why can inflation hurt creditors?

Answer 31

Think of it this way: If you are a creditor lending out money at a fixed rate, inflation cuts into the percentage that you are actually making. If you lend out money at 7% a year, and inflation is 5%, you are only really clearing 2%.

Question 32

How would the following affect the interest rates? U.S. bombers attack Iraq (again). The President is impeached and convicted.

Answer 32

While it can’t be said for certain, chances are that these kind of events will lead to fears that the economy will go into recession, so the Fed would want to balance that by giving expansionary signals and lowering interest rates.

Question 33

What does the government do when there is a fear of hyperinflation?

Answer 33

The government has fiscal and monetary policies it can use in order to control hyperinflation. The monetary policies (the Fed’s use of interest rates, reserve requirements, etc.) are discussed in detail in this chapter. The fiscal policies include the use of taxation and government spending to regulate the aggregate level of economic activity. Increasing taxes and decreasing government spending slows down growth in the economy and fights inflationary fears.

Question 34

How would you value a perpetual zero coupon bond?

Answer 34

The value will be zero. A zero coupon doesn’t pay any coupons, and if that continues on perpetually, when do you get paid? Never - so it ain’t worth nothing!

Question 35

Let’s say a report released today showed that inflation last month was very low. However, bond prices closed lower. Why might this happen?

Answer 35

Bond prices are based on expectations of future inflation. In this case, you can assume that traders expect future inflation to be higher (regardless of the report on last month’s inflation figures) and therefore they bid bond prices down today. (A report which showed that inflation last month was benign would benefit bond prices only to the extent that traders believed it was an indication of low future inflation as well.)

Question 36

What does the yield curve look like? Why?

Answer 36

Yield curve is a visual representation of the term structure of interest rates. Upward sloping – three theories on what the shape tells us:

(1) Expectations Theory – the hypothesis that long-term interest rates contain a prediction of future short-term interest rates. Expectations theory postulates that you would earn the same amount of interest by investing in a one-year bond today and rolling that investment into a new one-year bond a year later compared to buying a two-year bond today.
(2) Liquidity Preference Theory – The idea that investors demand a premium for securities with longer maturities, which entail greater risk, because they would prefer to hold cash, which entails less risk. The more liquid an investment, the easier it is to sell quickly for its full value
(3) Market Segmentation – different investors have different preferences so each trades separately.

Approximately: curve is flat for next six months.

1yr: 0.15%
5yr: 0.87%
10yr: 1.98%
30yr: 3.14%

Question 37

Say you have a normal bond that you buy at par and you get the face amount at maturity. Is that most similar to buying a put, selling a put, buying a call or selling a call?

Answer 37

You can liken it to selling a put because if the stock decreases in value, you lose money, like a bond defaulting. But if its neutral, you’re neutral in both cases.

Question 38

You have a company with $500 million of senior debt and $500 million of junior debt. The senior debt has an interest rate of L+ 500 and, in default, would recover 70 percent; the junior debt would recover 30 percent in default. What should the interest rate be on the junior debt?

Answer 38

Loss on default * Probability of default = incremental interest that needs to be paid. So 70 percent loss * 5 percent probability (an assumption you have to make) = 350 basis points over the senior debt or L + 850.