1. You’ve borrowed $20,000 on margin to buy shares in Disney, which is now selling at $40 per share. Your account starts at the initial margin requirement of 50%. The maintenance margin is 35%. Two days later, the stock price falls to $35 per share.
a. Will you receive a margin call?
b. How low can the price of Disney shares fall before you receive a margin call?
a.because the initial margin requirement is 50%，so totally I have $40000 to buy
shares. And that causes I own 1000 shares.
Margin%=(1000x35-20000)/35000=42.9%
b.assume the price as P.
（1000P—20000）/1000P=35%
Getting the value of P is $30.77.
（35*1000-20000）/35*1000=3/7>35%，不会受到margin call
2. 某封闭式基金年初资产净值是12.00美元/单位，年末资产净值为12.10美元/单位。年初时基金按资产净值的2%溢价出售，年末时基金按照资产净值的7%折价销售，该基金支付了1.5美元的年终收入和资本利得，则基金投资者本年度的收益率是多少？
Rate of return=（12.10x0.93-12.00x1.02+1.5）/(12.00x1.02)=0.042=4.2%
3. IBM股票的当前价格信息为：买方报价：19.95美元; 卖方报价：20.05美元。你发出一条20美元的止损指令，
意味着你在向经纪人传递什么意思？你的指令会被执行吗
在传递，一有盈利空间就执型的指令。会被执行，因为当要卖出股票时，关注买方报价，20比当前的19.95要高这就表示有盈利空间。而当要买入股票时，关注卖方报价，20比20.05要低，买入有盈利空间。
止损卖出指令，一旦股价跌破20立即执行，执行
止损买入指令，一旦股价涨到20立即执行，执行
4. On January 1, you sold short one round lot (that is, 100 shares) of Zenith stock at $14 per share.
On March 1, a dividend of $2 per share was paid. On April 1, you covered the short sale by buying the stock at a price of $9 per share. You paid 50 cents per share in commissions for each transaction. What is the value of your account on April 1?
1400-900-0.5x100x2-2x100=200
借股票100股，
第三次作业
1. An analyst estimates that a stock has the following probabilities of return depending on the state of the economy:
What is the expected return of the stock?
E(r)=∑p(s)r(s)=0.1x15%+0.6x13%+0.3x7%=11.4%
2. Consider the following information about a risky portfolio that you manage, and a risk-free asset：E(r P) = 11%, σp = 15%, r f = 5%.
(1). Your client wants to invest a proportion of her total investment budget in your risky fund to provide an expected rate of return on her overall or complete portfolio equal to 8%. What proportion should she invest in the risky portfolio, P, and what proportion in the risk-free asset?
Assume proportion in risky portfolio is y
E(R)=(1-y)rf+yE(rp)=(1-y)x5%+yx11%=8%
6%y=3%
y=50%.
So the proportion in risky portfolio and risk-free asset is both 50%.
margin rate(2). What will be the standard deviation of the rate of return on her portfolio?
STD=σc=yσp=50%x15%=7.5%
(3). Another client wants the highest return possible subject to the constraint that you limit his standard deviation to be no more than 12%. Which client is more risk averse?
7.5%<12%.
The former one(7.5%) is more risk averse.
Because the higher std is, the more risk averse existed.
1. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 8%. The probability distribution of the risky funds is as follows:
Expected Return  Standard Deviation
Stock fund (S)    20%          30%
Bond fund (B)    12%          15%
The correlation between the fund returns is 0.10.
(1). What are the investment proportions in the minimum-variance portfolio of the two risky funds, and what is the expected value and standard deviation of its rate of return?
ρ=cov（x，y）/（std（X）std（Y））
Cov(rS,rB)=ρxσSσB=0.1x0.3x0.15=0.45%
W（s）min=(Var（rB）-Cov(Rs,rB)）/（Var(rS)+Var（rB）-2Cov（rS，rB））=(15%^2-0.45%)/(30%^2+15%^2-2x0.45%)
=1.8%/10.35%≈17.39%
W(B)min=1-W（s）=82.61%
【(Var（rS）-Cov(rs,rB)）/（Var(rS)+Var（rB）-2Cov（rS，rB））】
=(30%^2-0.45%)/(30%^2+15%^2--2x0.45%)
=8.55%/10.35%≈82.61%
E(rp)=wsE(rs)+wbE(rb)=17.39%x20%+82.61%x12%=3.478%+9.9132%=13.3912% σp=（wS^2σS^2+wB^2σB^2+2wSwBσS,B)^1/2
=（17.39%^2x30%^2+82.61%^2x15%^2+2x17.39%82.61%0.45%)^1/2
=（0.272%+1.535%+0.129%)^1/2=(1.936%)^1/2≈13.9%
(2). What is the reward-to-volatility ratio of the best feasible CAL?
ws=[(E（rs）-rf)σb^2-(E(rb)-rf)Cov(Rs,Rb)]/[( E(Rs)-rf)σb^2+(E(Rb)-rf)σs^2-
[E(Rs)+E(Rb)-2rf]Cov(Rs,Rb)]
=[(20%-8%)x15%^2-(12%-8%)x0.45%]/[( 20%-8%)x15%^2+(12%-8%)x30%^2-(20%+12%-2x8%)0.45%]
=(0.27%-0.018%)/(0.27%+0.36%-0.072%)
=0.252%/0.558%
=45.16%
Wb=1-Ws=54.84%
E(rp)=45.16%x20%+54.84%x15%=15.61%
σp=（wS^2σS^2+wB^2σB^2+2wSwBσS,B)^1/2
=（45.16%%^2x30%^2+54.84%^2x15%^2+2x45.16%54.84%0.45%)^1/2
=16.54%
Sp=(E（rp）-rf)/σp=（15.61%-8%）/16.54%≈0.46
(3). You require that your portfolio yield an expected return of 14%, and that it be efficient, on the best feasible CAL.
a. What is the standard deviation of your portfolio?
b. What is the proportion invested in the T-bill fund and each of the two risky funds?
a、

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