紧急求助几道题目

1. Suppose the 12 month T.bill rate in the UK is 8% and that in the US is 5%. The current UK/US spot rate is .75. If there were no transactions costs, what would the twelve month forward rate be? Would forward Sterling be at a premium or a discount? If it costs 1% in commission to operate in the foreign exchange (FOREX) spot and futures markets and another 1% to purchase T.Bills, what bands would you expect the forward rate, the forward premium and the CD to lie in, respectively?

Using a similar argument as that given above, show that the upper bound for the CD is +2%.

N.B. you may use the approximations given in the lectures if you wish

2. Show that the UIP and CIP hypotheses can be combined to imply that

st+1 ≈ a0 + a1ftt+1 + εt+1

where εt is an error and where all symbols are as defined in the lecture.

Under UIP/CIP what properties does the error term have?

What values would a0 and a1 have? Can we test whether these values hold using simple linear regression applied to the above? If not why not and what reformulation would you suggest?

3. The Euler equation from the CCAPM model for some asset i in lecture 3 was

For convenience write

i) show that under log utility (u=log(C)), M is inversely related to the growth rate of consumption

Using the definition cov(x,y) = E(xy)-E(x)E(y) and noting that pit+1/pit is the gross return on asset i

ii) show that the expected return on the asset varies negatively with its (conditional) covariance with consumption growth. Give some intuition as to why this is so.

M is called the stochastic discount factor…..

Suppose now that the asset paid an explicit stochastic dividend of dit+j in period t+j, j=1,2……so that the Euler condition can be written as

Suppose for simplicity that the stochastic structure of M was such that it had constant conditional covariances with dividends and prices.

iii) Rewrite the above using the covariance definition formula also given above.

Now suppose that for simplicity’s sake the stochastic structure of consumption was such that Et(Mt+1)≈M where M is constant.

iv) Show that the asset price is the net present value of the future stream of dividends. Explain the role of M.

v) What sort of consumption time series behaviour would imply Et(Mt+1) ≈M where M is constant?

vi) In the light of all of the above and in the light of the CCAPM lecture discuss the role played by the covariance of M with dividends in pricing an asset.

4. The U.K. government issues both inflation-indexed (real) and non-indexed (nominal) bonds, allowing both real and nominal yield curves to be constructed. Suppose that the yields on one-year and two-year real and nominal bonds in year t, are

Maturity Real Nominal

1 year 2% 5%

2 year 3% 7%

Under the pure expectations theory of the term structure, what is the annual inflation rate expected for year t+1, ?

5. Suppose the participants in financial markets are risk neutral and can costlessly undertake arbitrage activity. Also assume that the pure expectations theory of the term structure holds.

a. Suppose that it is April 1997 and that the UK nominal yield curve is flat and the yield to maturity is 10% at all maturities, what is expected to happen to short-dated nominal yields in future?

b. In May 1997 the newly elected Labour government passed legislation which gave operational control of monetary policy to the Bank of England and assigned the Bank an inflation target of 2.5%. Assume that the legislation enhanced the ‘credibility’ of the monetary authority.

i. If the short-dated real yield is 2.5% at all maturities, at all points in time, what should happen to the nominal yield curve immediately after the legislation was introduced?

ii. What does your post-legislation nominal yield curve indicate about the expected behaviour of short-dated nominal interest rates?

6. Suppose that the nominal yield curve in a certain country is hump-shaped (first upward sloping, then downward sloping).

i. What is expected to happen to short-dated yields in future?

ii. Assuming that (output) prices adjust sluggishly, what might be expected to happen to economic activity, given the hump-shaped yield curve?

7.

i. Under what conditions can a stock price be written as the net present value of future discounted expected dividends with constant discount rates?

ii. In Shiller’s (American Economic Review, 1981) terminology, what is the ex post rational stock price?

iii. Show that, under Rational Expectations, the variance of the ex post rational price should be greater than the variance of the actual stock price.

iv. What computation and other difficulties arise when examining the volatilities in iii)?

8. Assume the real ex ante short term interest rate is constant and equal to the nominal interest rate plus expected inflation. In a market clearing model where prices are fully flexible show with the aid of graphs what the effects of an unanticipated and fully credible decline in money growth on the nominal yield curve and the price level will be. Are these effects what we see in practice and if not why not?

9. Is there a “classical” shape for the yield curve and if so why?” What does it mean in relation to this to say the yield curve is “inverted”?

10. Calculate the yield to maturity (% per annum) on a two year bond with face value of £100 that pays an annual coupon of £1 in each of the two years and that is issued at a price of £90.

一题20个币~~~紧急求助，2个小时内有效~~~拜托了