Chapter 13: Term structure of interest rates

Question 1

Yield to maturity

Answer 1

yield or yield to maturity for a bond.
the AER that satisifes the bond’s equation of value

Price = PV of coupons + PV of redemption payment

Question 2

spot rate

Answer 2

the t year spot rate s_t is the Annual effective yield on a t=year zero-coupon bond.

It represents the annual effective return on an investment made now that is to be repaid as a lump sum with interest at time t years

Question 3

method for determining spot rates of a bond

Answer 3

1. Calculate the prices of the bonds of different durations based on their yields
2. Set s_1 equal to the yield of the bhond paying a single cashflows at time 1
3. s_2, based on the price of the bond maturing at time 2 and s_1
4. Find s_3 based on the price of the bond maturing at time 3, and s_1 and s_2
5. And so on
   6.

Question 4

(spot rate) yield curve

Answer 4

Graph of spot rates agains thteir maturities.

spot rates generally higher than yields as yield is a weighted average of spot rates.
At 1 they are equal

Question 5

r-year forward rate

Answer 5

f_t,r, rate that applies from t to t+r.
AER that could be used to accumulate a sum of money from t to t+r or to discount from t+r to t

annual effective rate of return that can be earned on an investment made at t years, that is to be repaid as a lump sum with interest at time t+r.

f_0,r=s_r
f_t,1=f_t (one-year forward rate)

Question 6

par yield

Answer 6

The n-year par yield is defined as the annual coupon rate such that an n-year bond, which is redeemable at par, has a price of £100 per £100 nominal, where the price is calculated using the spot and/or forward rates available.

theoretical measure which gives an overall indication of the yield on bhonds of a given duration

Question 7

Expectations theory

Answer 7

the current yield curve reflects the market’s expectation of the future level of interest rates within the economy.

Suppose the general view amongst investors is that interest rates will rise in the future. => investors will also expect the yield on bonds to increase (otherwise bonds would be uncompetiitive compared to other investments available)
if yields will increase, investors:
* won;t buy longer term bonds now, asx this will lock them into the current, lower yield. Since investors do not wish to buy longer-term bonds, the price of such bonds will fall, casugint he yield on them to rise (as thoss buying those bonds will be paying less to recieve the same cashflows)
* will buy shorter-term bonds, because by the time these bonds amture, investors will be ready to purchase new bonds benefitting from the higher yield expected in the future. Since investors wish to buy shorter-term bonds, the price of such bonds will rise, causing the yield on them to fall (as those buying these bonds will be paying more to recieve the same cashflows)

So if interest rates are expected to increase ==> yield on shorter-term bonds will decrease and on longer term bonds icnrease creeating an upward sloping curve

Question 8

liquidity

Answer 8

the speed and certainty with which cash value of an investment can be realised

Question 9

liquidity preference theory

Answer 9

Most government bonds and those issued by large companies can be sold relatively quicjkly as there tends to be many investors interested in puirchasing them.

The price at which they can be sold tho is less certain as that depends on interest rates, and they vary over time.

Longer term bonds are more affected by interest rate changes, meaning the price is less certain and so longer term bonds are less liquid.

LPT states that investors prefer more liquid assets as their values fluctuate less, and this influences the shape of the yield curve.

In particular, to compensate investors for the risk and uncertainty of investingf in less liquid longer-term bonds, they require some additional return on those bonds. this can explain some of the excess return on longer-term bonds over shorter-term bonds, and goes some way to explaining an upward sloping yield curve.

Question 10

market segmentation theory

Answer 10

attempts to explain the shape of the yield curve by splitting it up into different segments (such as shorter and longer term) and then considers supply and demand in each segment separately.

Long term: purchased by investors with longer cashflows; pension providers, life insurance
short term: general insurance companies and banks.

Each segment is affected by things affecting that area