寫作批改
VIP與詳解卡管理
, which is a function of the
covariance between the operating profit at t = 1 of firm y and the aggregate productivity shock.試卷測驗 - 110 年 - [無官方正解]110 國立臺灣大學_碩士班招生考試_財務金融研究所乙組:財務管理與財金數學(含微分方程、線性代數)#102120-阿摩線上測驗
a0908002698剛剛做了阿摩測驗，考了100分
【客服暫停服務時間】2024/05/01(三)，影響：阿摩粉絲團、系統回報、信箱、鑽石兌換商城出貨事宜。
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Based on NPV, which project would you choose if the opportunity cost of capital is 12%? 2. (15 points) To construct a portfolio using the mean-variance framework, one needs cstimates of the expected return r, the variance σ2i and the co-variance aj for each stocks, j. Forn stocks, you have to estimate a total of n(n-1)/2 correlation coefficients. Single index models are used, to reduce this hugc amount of needed estimates. Now we are going to construct a portfolio with two assets using the single index model.
(1) (3 points) Please calculate the mean and variance of the stock index return and mean return for asset B.
We run the following regression for each asset.
(3) (4 points) A Single Index Model (SIM) specifies two sources of uncertainty for a security's
21.078
return: Systematic risk and firm-specific risk
Return variance Systematic risk
Firm-specific risk
(4) (6 points) Now assuming a portfolio with weights for asset A and asset B are 0.7 and 0.3.
Plcase find out E(rp) and 
. 
(2) (1.5 point) The payoff to equity investors, on liquidation, can therefore be written as: Payof
where, V = Value of the firm
D = Facc Value of the outstanding debt and other external
Please draw a figure of the payoff to equity investors (Y-axis) and the firr value (X-axis).
(3) (1.5 point) The payoff to equity investors, on liquidation, can therefore be written as: Payoff
where, V = Value of the firm
D = Face Value of the outstanding debt and other external
Piease draw a figure of the payoff to debt investors (Y-axis) and the firm value (X-axis)
(4) The relationship between equity/debt and firm value can be described by the following assets,
call option, put option, and pure bond. Please fill in the correct position (long, short, or NO)
for an investor to take to desctribe the relation between equity/debt and firm value. (3 points)
Please explain tour reasons. (2 points)
Put option
第二部分:財金數學
1. (5 points) Consider the system of following questions
where x1, x2, x3 are unknown. Please use the matrix-vector product to express the 3 x 3 linear
system
4. Consider a two-period economy (/ = 0, 1). The operating profit of firm j can be expressed as
is the exogenous profitability shock; At is a technology shook at time
t;
is private capital of fimm j. a ＞ 0 is assumed. The depreciation rate of capital k for firm / is
δj. Thus, the investment of firm
, firm j has a liquidation
value of
. The investment in private capital involves adjustment cost 
. The stochastic discount factor between time 0 and 1 is m, where log(m) = logβ + γ(x0 -x1), where 0 ＜β＜ 1, and γ＞ 0. Firm j then chooses ij.0 to maximize its value, which is the sum
of the discounted cash flows from the two periods:
E[.] is an expectation operator. From standard asset pricing equation, 
-Cov0(r1,m). Specifically, the cash flows from t = 0 are equal to the operating profit minus the
investment cost and the adjustment cost. The cash flows from ! = I are equal to the operating
profit plus the liquidation value.
(2) (10 points) Note that the investment return
, defined as the ratio of marginal benefit to
marginal cost of investment, is equal to the firm's stock return (rl) under equilibrium. Please
show that 