作者rogerhsiao (那又怎样)
看板NTU-Exam
标题[试题] 96下 陈其美 投资学 期末考
时间Sat Jun 21 19:35:43 2008
课程名称︰投资学
课程性质︰必修
课程教师︰陈其美
开课学院:管理学院
开课系所︰财金系
考试日期(年月日)︰97年6月20日
考试时限(分钟):180
是否需发放奖励金:是
(如未明确表示,则不予发放)
试题 :
Part I, True-False Questions. (40%)
1. Recent studies of stock market prices using US data found that
long-horizon returns are positively serially correlated, while short- or
intermediate-horizon returns are negatively serially correlated.
2. The yield to maturity of a bond diers from the current yield of
the bond; the latter is the bond's annual coupon payment divided by
the bond price.
3. Advocates of the liquidity preference theory of the term struc-
ture believe that short-term investors dominate the market so that the
foward rate will generally fall short of the expected short rate.
4. According to James Tobin, the ratio of market price of a rm's
equity to the replacement cost of its assets less its liabilities, or the
Tobin's q, will tend toward 1 in the long run.
5. A short straddle is established by buying a call and a put on a
stock, each with the same exercise price and the same expiration date.
A strap is a variation of a straddle, involving two calls and one put.
6. The Black-Scholes option pricing formula has a surprising feature:
the option value does not depend on the expected rate of return on the
underlying asset (the stock).
7. The open interest on a futures contract is the number of contracts
outstanding, where long and short positions are counted separately, but
the clearinghouse's position is not counted in the computation of open
interest.
8. Since 2002 OneChicago has operated an entirely electronic market
in single-stock futures, but trading volume in this market has to date
been disappointing.
9. Sharpe's and Treynor's measures both give excess return per unit
of risk on a mutual fund, but the former considers only the systematic
risk.
10. Convergence arbitrage means to buy one security and sell the
other, with the belief that at a given date the pricing discrepencies
between the two securities almost necessarily must disappear. This
was a strategy extensively used by Long-Term Capital Management.
Part II, Computations. (Important Instruction: You must (i) detail
all the computations and (ii) give a precise solution to each problem. You
will not receive any credit if you simply write down an equation without
obtaining the nal result.)
1. (30%) Consider a three-date (dates 0, 1 and 2) economy with perfect
nancial markets. There are four possible states ( = w1; w2; w3; w4).
At date 0, investors only know that the true state is an element of
, and the true state will be revealed perfectly at date 2. At date 1,
the occurrence or non-occurrence of the event E = w1; w2 becomes
publicly known. This is the standard event tree that we considered in
Lecture 5A. We assume that markets are dynamically complete. The
following table gives the price process of asset 1, denoted by p1, and
the forward price process for the delivery of one unit of asset 1 at date
2, which is denoted by G.
Asset price/(Date,Event)
(0;omega ) (1;E) (1;Ec) (2; w1) (2; w2) (2; w3) (2; w4)
p1 100 110 90 150 114 134 100
G 624/5 132 117 150 114 134 100
At date 0, two default-free coupon bonds, referred to as X and Y, are
traded, and their data are summarized in the following table (where
the date-0 bond prices are obtained after the date-0 coupon payments
are made; see Lecture 7, Part I):
bond maturity coupon payment face value date-0 price
X date 1 50 1000 x
Y date 2 200 1000 y
(i) Compute x and y.
(ii) Mr. B is endowed with 1 million dollars (a sure income!) at date
2. He only wants to consume at date 1, and he wants to consume the
same amount in event E and in event Ec. Suppose that he is allowed
to trade the above two bonds X and Y only, and he is allowed to trade
only at date 0. At date 0, how many units of bond X should Mr. B
buy or sell, and how many units of bond Y should Mr. B buy or sell?
How much can Mr. B consume at date 1?
(iii) At date 0, what is the futures price for the delivery of one unit of
asset 1 at date 2?
2. (30%) Consider a three-date economy with the same event tree as de-
scribed in Problem 1 above; that is, markets are dynamcially complete,
with the following table giving the price process p1 of asset 1 and the
forward price process G for the delivery of one unit of asset 1 at date
2.
Asset price/(Date,Event)
(0;omega ) (1;E) (1;Ec) (2; w1) (2; w2) (2; w3) (2; w4)
p1 100 110 90 150 114 134 100
G 624/5 132 117 150 114 134 100
Consider a European call option (with price denoted by c) written on
one unit of asset 1 with date 2 being the expiration date and exercise
price being 126. Assume that one-period deposit (the riskless one-
period money market account) is available for trading at both dates 0
and 1.
(i) Find c(0), c(1;E) and c(1;Ec); and
(ii) Suppose that the date-0 option price prevailing in the market is
actually greater than the c(0) that you computed in part (i). Find a
dynamic arbitrage strategy that involves trading only in asset 1, the
riskless one-period money market account, and the call option.
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