【正文】 INPUTS OUTPUT N I/YR PV FVPMTb. Use EAR = % as the annual rate in your calculator:What’s the PV of this stream?010015%2 3100 100You are offered a note which pays $1,000 in 15 months (or 456 days) for $850. You have $850 in a bank which pays a % nominal rate, with 365 daily pounding, which is a daily rate of % and an EAR of %. You plan to leave the money in the bank if you don’t buy the note. The note is riskless.Should you buy it?3 Ways to Solve:1. Greatest future wealth: FV2. Greatest wealth today: PV3. Highest rate of return: Highest EFF%iPer =% per day.1,0000 365 456 days8501. Greatest Future WealthFind FV of $850 left in bank for15 months and pare withnote’s FV = $1,000.FVBank = $850()456= $ in bank.Buy the note: $1,000 $.456 850 0 INPUTSOUTPUTN I/YR PV FVPMTCalculator Solution to FV:iPer = iNom/m= %/365= % per day.Enter iPer in one step.2. Greatest Present WealthFind PV of note, and parewith its $850 cost:PV= $1,000/()456= $. 456 .018538 0 1000 INPUTSOUTPUTN I/YR PV FVPMTPV of note is greater than its $850 cost, so buy the note. Raises your wealth.Find the EFF% on note and pare with % bank pays, which is your opportunity cost of capital: FVn= PV(1 + i)n $1,000 = $850(1 + i)456Now we must solve for i.3. Rate of Return 456 850 0 1000 % per day INPUTSOUTPUTN I/YR PV FVPMTConvert % to decimal:Decimal = EAR = EFF%= ()365 1 = %.Using interest conversion: P/YR =365NOM% =(365)= EFF% =Since % % opportunity cost,buy the note.CHAPTER 3 Risk and Return? Basic return concepts? Basic risk concepts? Standalone risk? Portfolio (market) risk? Risk and return: CAPM/SMLWhat are investment returns?nInvestment returns measure the financial results of an investment.nReturns may be historical or prospective (anticipated).nReturns can be expressed in:lDollar terms.lPercentage terms. What is the return on an investment that costs $1,000 and is soldafter 1 year for $1,100?nDollar return:nPercentage return:$ Received $ Invested $1,100 $1,000 = $100.$ Return/$ Invested $100/$1,000 = = 10%.What is investment risk?nTypically, investment returns are not known with certainty.nInvestment risk pertains to the probability of earning a return less than that expected.nThe greater the chance of a return far below the expected return, the greater the risk.Probability distributionRate ofreturn (%) 5015020Stock XStock Yn Which stock is riskier? Why?Assume the FollowingInvestment AlternativesEconomy Prob. TBill HT Coll USR MPRecession % % % % %Below avg. Average Above avg. Boom What is unique about the Tbill return?nThe Tbill will return 8% regardless of the state of the economy.nIs the Tbill riskless? Explain.Do the returns of HT and Collections move with or counter to the economy?? HT moves with the economy, so it is positively correlated with the economy. This is the typical situation.? Collections moves counter to the economy. Such negative correlation is unusual.Calculate the expected rate of return on each alternative.r = expected rate of return.rHT = (22%) + (2%) + (20%) + (35%) + (50%) = %.^^n HT has the highest rate of return. n Does that make it best?rHT %Market USR Tbill Collections ^What is the standard deviationof returns for each alternative??Tbills = %.?HT = %.?Coll =%.?USR =%. ?M=%.HT:? = ((22 ) + (2 ) + (20 ) + (35 ) + (50 ))1/2 = %.Prob.Rate of Return (%)TbillUSR HT0 8 ? Standard deviation measures the standalone risk of an investment.? The larger the standard deviation, the higher the probability that returns will be far below the expected return.? Coefficient of variation is an alternative measure of standalone risk.Expected Return versus RiskExpectedSecurity return Risk, ?HT % %Market USR Tbills Collections Coefficient of Variation:CV = standard deviation/Expected return.CVTBILLS = %/% = .CVHIGH TECH = %/% = .CVCOLLECTIONS = %/% = .. RUBBER = %/% = .CVM = %/% = .Expected Return versus Coefficient of VariationExpected Risk: Risk:Security return ? CVHT % % Market USR Tbills Collections Return vs. Risk (Std. Dev.): Which investment is best?Portfolio Risk and ReturnAssume a twostock portfolio with $50,000 in HT and $50,000 in Collections.Calculate rp and ?p.^Portfolio Return, rprp is a weighted average:rp = (%) + (%) = %.rp is between rHT and rColl.^^^^^ ^^ ^rp = ?? wiri?ni = 1Alternative Methodrp = (%) + (%) + (%) + (%) + (%) = %.^Estimated Return(More...)Economy Prob. HT Coll. Port.Recession % % %Below avg. Average Above avg. Boom ? ?p = (( ) + ( ) + ( ) + ( ) + ( ))1/2 = %.? ?p is much lower than:– either stock (20% and %).– average of HT and Coll (%).? The portfolio provides average return but much lower risk. The key here is negative correlation.TwoStock Portfolios? Two stocks can be bined to form a riskless portfolio if r = .? Risk is not reduced at all if the two stocks have r = +. ? In general, stocks have r ? , so risk is lowered but not eliminated.? Investors typically hold many stocks.? What happens when r = 0?What would happen to therisk of an average 1stockp