# FAU FIN 3403 Risk and Return (Students) - Risk and Return...

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Risk and ReturnRates of ReturnHolding Period ReturnAssume you buy a stock in year t-1 and hold it until year t, and it pays adividend, dt.Then the one-period holding return can be figured as follows:RtPt– Pt-1+ dt/ Pt-1or= Pt– Pt-1/ Pt-1if dt= 0.This is for 1 year.What if we held a stock for more than a year?We couldcompute this either using an arithmetic average return or a compound rate ofreturn.Naturally, in finance we prefer the latter, the former being calculatedby taking the simple average of the annual holding period returns.eg.Price of stock at end of year, first paying no dividend, then paying adividend:PriceReturnWhat if d≠0Return w/dividendPt=20Rt20 -15 / 15 = .3333.75.383Pt-1= 15Pt-2= 10Rt115 – 10 / 15 = .5.5.55Pt-3= 14Rt210 – 14 / 14 = -.286.25-.268IF there are no dividends, we could calculate this with a FinancialCalculator:PV = -14FV = 20PMT = 0I = ? = 12.62N = 3But this only works when there are no intermediate cash flows, i.e., whenthere are no dividends.So, in general we need to use the GMR.
Geometric Mean Return1111nntttRGMRWhere:is the product operator similar to a summation operator.That is:32131XXXjjXThen the GMR (for the without dividend example) is:1)714)(.5.1)(3333.1(31GMRt= 1.126 – 1 = .126 or 12.6%Notice that the .714 comes from 1+(-.286)=.714.Note 1:It makes no sense to calculate a simple return over the whole periodunless you want to see how much you have made on your money over thewhole period.%9.42141420RtNote 2:This is similar if we want to calculate the growth in, say, earnings ordividends per share.That is, if we have data on earnings per share over 5

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