International Bond and Currency Markets: Tutorial Problem Set 6 Solutions | Exercises Financial Market

International Bond and Currency Markets C39SM1

Tutorial Problem Set 6

Solutions

1. Spot interest rate is the interest rate which applies today (current rate). Forward interest rate is

the interest rate agreed today, which will apply to investment or loan starting at some future date.

Future spot interest rate is the spot rate that will apply in the future (but we do not know it until the

time passes by and we reach certain point of time in the future to which it applies). Future expected

spot interest rate is the interest rate that is currently expected to apply in the future.

2. (a) Yield curve has yield on vertical axis and maturity of bond on horizontal. Hence to answer

part (a) simply read off the yield on the yield curve corresponding to maturity = one year.

(b) To handle forward contracts, note that the points on the yield curve correspond to the spot rates:

0s1, 0s2, 0s3, 0s4, etc. To calculate the interest rate on a forward contract to buy a one-year bond one

year from now, what we need is the forward interest rate 1f2. This is calculated by using the

relationship:

(1 + 0s1)x(1 + 1f2) = (1 + 0s2)2.

Using this gives the answer to (i) and very similar formulae give the answers to (ii) and (iii):

(1 + 0s2)2x(1 + 2f3) = (1 + 0s3)3

(1 + 0s3)3x(1 + 3f4) = (1 + 0s4) 4.

These relationships hold because they represent different routes to achieving a contract over a given

period, and should come out with the same combined return - otherwise there would be arbitrage

opportunities which investors would spot and compete away.

3. It is true that forward rates are often poor predictors in that future spot rates turn out differently.

But if we are devising an investment policy now, then by definition we don’t know what future spot

rates will be - and the currently available futures rates represent the best information we have to

hand. Another relevant issue here is: are current futures rates biased predictors of the future spot

rates or do we observe errors in both directions with more or less equal probability? In the latter

case, use of futures rates is OK; but in the former, we might want to think about how to deal with

systematic biases.

4. The efficient markets theory (EMH) claims that if the markets are efficient then it is not possible

to forecast the future prices based on any past or current information. Hence, when we know that

the forward rates (which are the “current information”) are not perfect predictors of future spot

rates, this might lead to the conclusion that the markets are efficient. This is obviously a paradox,

because failure of accurate prediction of future spot rates by the current forward rates does not

necessarily have to imply market efficiency. We still can be successful in forecasting the movement

of interest rates in the future (and based on that construct profitable trading strategies beating the

market) even if the forward rates are not exactly accurate. It is important that they indicate the

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International Bond and Currency Markets C39SM

Tutorial Problem Set 6

Solutions

Spot interest rate is the interest rate which applies today (current rate). Forward interest rate is the interest rate agreed today, which will apply to investment or loan starting at some future date. Future spot interest rate is the spot rate that will apply in the future (but we do not know it until the time passes by and we reach certain point of time in the future to which it applies). Future expected spot interest rate is the interest rate that is currently expected to apply in the future.
(a) Yield curve has yield on vertical axis and maturity of bond on horizontal. Hence to answer part (a) simply read off the yield on the yield curve corresponding to maturity = one year.

(b) To handle forward contracts, note that the points on the yield curve correspond to the spot rates: 0 s^1 ,^0 s^2 ,^0 s 3 ,^0 s^4 , etc. To calculate the interest rate on a forward contract to buy a one-year bond one year from now, what we need is the forward interest rate 1 f 2. This is calculated by using the relationship: (1 + 0 s 1 )x (1 + 1 f 2 ) = (1 + 0 s 2 )^2. Using this gives the answer to (i) and very similar formulae give the answers to (ii) and (iii): (1 + 0 s 2 ) 2 x (1 + 2 f 3 ) = (1 + 0 s 3 )^3 (1 + 0 s 3 ) 3 x (1 + 3 f 4 ) = (1 + 0 s 4 ) 4. These relationships hold because they represent different routes to achieving a contract over a given period, and should come out with the same combined return - otherwise there would be arbitrage opportunities which investors would spot and compete away.

It is true that forward rates are often poor predictors in that future spot rates turn out differently. But if we are devising an investment policy now, then by definition we don’t know what future spot rates will be - and the currently available futures rates represent the best information we have to hand. Another relevant issue here is: are current futures rates biased predictors of the future spot rates or do we observe errors in both directions with more or less equal probability? In the latter case, use of futures rates is OK; but in the former, we might want to think about how to deal with systematic biases.
The efficient markets theory (EMH) claims that if the markets are efficient then it is not possible to forecast the future prices based on any past or current information. Hence, when we know that the forward rates (which are the “current information”) are not perfect predictors of future spot rates, this might lead to the conclusion that the markets are efficient. This is obviously a paradox, because failure of accurate prediction of future spot rates by the current forward rates does not necessarily have to imply market efficiency. We still can be successful in forecasting the movement of interest rates in the future (and based on that construct profitable trading strategies beating the market) even if the forward rates are not exactly accurate. It is important that they indicate the

correct direction of change of the interest rates in the future. If such investment strategies can consistently generate the profits above the market averages (as the EMH theory states), then this would lead to the opposite conclusion, i.e. that the markets are not efficient.

(a) 0 s 1 = 0.06, 0 s 4 = 0.075, and 0 s 5 = 0.08. The required rate is 1 f 4 , and this is derived from the equation: (1 + 0 s 1 )x(1 + 1 f 5 ) 4 = (1 + 0 s 5 ) 5. This should then give the stated result of 0.0851 (=8.51%).

(b) Here we are trying to find 4 f 5 and we do so by making use of the equation: (1 + 0 s 4 ) 4 x (1 + 4 f 5 ) = (1 + 0 s 5 )^5. The solution is: 10.02%.

(c) Using the new rates: 0 s 1 = 0.05, 0 s 4 = 0.06, and 0 s 5 = 0.07, we must solve for 1 f 5 the equation: (1 + 0 s 1 )x (1 + 1 f 5 ) 4 = (1 + 0 s 5 )^5. The solution is: 7.51%.

The Pure Expectations Hypothesis (PEH) claims that forward rates equal the bond market’s expectations of future spot interest rates. The Liquidity Preference Theory (LPT) suggests that forward rates include both investors’ expectations of future spot rates and the liquidity premium. The Segmented Markets Hypothesis (SMH) explains the term structure of interest rates as a series of preference zones, which certain investors select depending on term to maturity (some investors often prefer particular maturities to match their liabilities). The Preferred Habitat Theory (PHT) claims that investors prefer to match bond maturity with planned expenditure, but preferred habitats not absolute.

International Bond and Currency Markets: Tutorial Problem Set 6 Solutions, Exercises of Financial Market

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