1、1.The Time Value of Money1.Interest rate:required rate of return,discounted rate,opportunity cost 2.Nominal interest rate=real risk-free interest rate +inflation premium +default risk premium +liquidity premium +Maturity premium3.EAR=(1+rs/m)m-1 rs=Ln.(1+HYR),EAR=ers-1 when continuous compoundingNom
2、inal risk free interest rate FV=PV(1+R)n Begin mode and End modePV=D/R and PV=D/(r-g)(present value of perpetuity),r is discounted rate,g growth rateNPV and IRRMoney-weight return(MWR)similar IRR:CF0+CF1/(1+MWR)+CFn/(1+MWR)N=0Time weighted return(TWR):=【(end value1/begin value1)(end value2/begin val
3、ue2).(end valuen/begin valuen】1/n-1 HPR=P1-P0+D1/P0Holding period yield(HPY)=(ending value/begin value)-1Bank discount yield (BDY)=(discount/face value)x(360/days to maturity)simple interestMoney market yield(MMY)=(discount/price)x(360/days to maturity)simple interestBond equivalent yield(BEY)=(disc
4、ount/price)x(365/days to maturity)simple interestEffective annual yield(EAY)=(1+HPY)365/days-1 compound interest2.Chebyshevs inequity:1-1/k2,k standard deviation调和平均：固定金额的投资购买股份的平均成本3.Mutually exclusive events,exhaustive events,independent events,dependent eventOdd for/odd against empirical probabil
5、ity priori probability/subjective probability ,Unconditional prob.conditional prob.(prob.of an event(A)conditioned on another event(B),denoted P(A|B)4.5.6.7.1.Over the past 240 months,an investors portfolio had a mean monthly return of 0.79%,with a standard deviation of monthly returns of 1.16%.Acco
6、rding to Chebyshevs inequality,the minimum number of the 240 monthly returns that fall into the range of 0.95%to 2.53%is closest to:A.80.B.107.C.133.2.You have developed a set of criteria for evaluating distressed credits.Companies that do not receive a passing score are classed as likely to go bank
7、rupt within 12 months.You gathered the following information when validating the criteria:Forty percent of the companies to which the test is administered will go bankrupt within 12 months:P(nonsurvivor)=0.40.Fifty-five percent of the companies to which the test is administered pass it:P(pass test)=
8、0.55.The probability that a company will pass the test given that it will subsequently survive 12 months,is 0.85:P(pass test|survivor)=0.85.A.What is P(pass test|nonsurvivor)?B.Using Bayes formula,calculate the probability that a company is a survivor,given that it C.passes the test;that is,calculat
9、e P(survivor|pass test).D.What is the probability that a company is a nonsurvivor,given that it fails the test?Is the test effective?8.3.A portfolio manager annually outperforms her benchmark 60%of the time.Assuming independent annual trials,what is the probability that she will outperform her bench
10、mark four or more times over the next five years?A.0.26B.0.34C.0.484.A stock is priced at$100.00 and follows a one-period binomial process with an up move that equals 1.05 and a down move that equals 0.97.If 1 million Bernoulli trials are conducted,and the average terminal stock price is$102.00,the
11、probability of an up move(p)is closest to:A.0.375.B.0.500.C.0.625.5.A call option on a stock index is valued using a three-step binomial tree with an up move that equals 1.05 and a down move that equals 0.95.The current level of the index is$190,and the option exercise price is$200.If the option val
12、ue is positive when the stock price exceeds the exercise price at expiration and$0 otherwise,the number of terminal nodes with a positive payoff is:A one.B.two.C.three.9.Allocation AAllocation BAllocation CExpected annual return6.5%7.5%8.5%Standard deviation of returns8.35%10.21%14.34%6.A client hol
13、ding a 2,000,000 portfolio wants to withdraw 90,000 in one year without invading the principal.According to Roys safety-first criterion,which of the following portfolio allocations is optimal?A.Allocation AB.Allocation BC.Allocation C7.Which sampling bias is most likely investigated with an out-of-s
14、ample test?A.Look-ahead bias B.Data-mining bias C.Sample selection bias8.An investor wants to maximize the possibility of earning at least 5%on her investments each year.Using Roys safety-first criterion,which of the following portfolios is the most appropriate choice?ExpectedStandardRoys Safety-Fir
15、stPortfolioreturndeviationvalue1 0.352 0.64322%40%10.9.An investor purchases one share of stock for$85.Exactly one year later,the company pays a dividend of$2.00 per share.This is followed by two more annual dividends of$2.25 and$2.75 in successive years.Upon receiving the third dividend,the investo
16、r sells the share for$100.The money-weighted rate of return on this investment is closest to:A.7.97%.B.8.15%.C.8.63%.10.An investor deposits 2,000 into an account that pays continuously compounded interest of 6%(nominal annual rate).The value of the account at the end of four years is closest to:12a
17、m11.The following end of month payments of$400,$700,and$300,(respectively)are due.Given a stated annual interest rate of 3.60 percent,the minimum amount of money needed in an account today to satisfy these future payments is closest to:9pm A.$1,308.B.$1,387.C.$1,391.12.The joint probability of returns,for securities A and B,are as follows:Return on security B=30%Return on security B=20%Return on security0.600A=25%Return on security00.40A=20%The covariance of the returns between securities A and B is closest to:10pm11.12.13.14.15.
