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FIN301CHAPTER11(2)

FIN301CHAPTER11(2) - 1-1 11-1 Ch 11 Risk Return Focus of Ch...

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1-1 11-1 Ch. 11: Risk & Return Focus of Ch. 11 more on price volatility/risk/pain for “futures” situations versus historical situations (latter being the focus of Ch. 10) Let’s begin our work by centering on Stock L Table 11.3 page 342 and calculating expected return of - 0.02 given perceived . 80 odds of a Recession and .20 odds of a Boom and related respective returns under each of these scenarios of -.20 and .70 1
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1-2 11-2 “Futures” Variance Calculation To calculate variance—top of page 344— we subtract from the indicated rate of return under each economic scenario the just-calculated expected return of -.02 (basically, we’re adding .02 here, right?)… proceeding to square each of these deviations and then multiplying each of the squared deviations by their respective scenario probabilities 2
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1-3 11-3 “Futures” Variance Calculation The sum of these 2 … and only 2 in this example … squared deviations multiplied by each of their respective scenario probabilities = the variance =.1296 Square root of the variance=standard deviation=0.36 Notice that when working with “futures” … and applying given probabilities to the square deviations … there’s no need to divide by N-1 3
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1-4 11-4 j i σ σ σ σ σ σ ij ij ij 2 i i port n 1 i n 1 i ij j n 1 i i 2 i 2 i port r Cov where j, and i assets for return of rates e between th covariance the Cov i asset for return of rates of variance the portfolio in the value of proportion by the determined are weights where portfolio, in the assets individual the of weights the W portfolio the of deviation standard the : where Cov w w w = = = = = + = ∑∑ = = = Switching our focus when calculating variance/standard deviation for a portfolio you need to use the following formula 4
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1-5 11-5 The key to this formula … … which is also shown on Blackboard as slide # 8 in the “Portfolio Standard Deviation” stack … is the covariance term Covariance measures the absolute degree to which the returns of 2 assets do or don’t move together, over time, relative to each of the 2 asset’s individual means As an aid to our understanding, let’s now look at a covariance calculation 5
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1-6 11-6 A sample covariance calculation Assume you have 2 securities A & B and that over the past three years per-year returns were, +15%, -20%, +20% (A) & -10%, +10%, -15% (B) It would appear at first glance that there’s a tendency for A to do well when B doesn’t do well If so, we could end up with negative covariance
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