# FINC19011 – BUSINESS FINANCE-Wk03-revised -...

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MODULE 3 (Wiley Resource - Chapter 7 – Customized  & Abridged) Dr. Tasadduq Imam

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Chapter 7 Risk and Return Prepared by Alex Proimos & Chee Jin Yap
Risk and return Future value vs. present value The greater the risk, the larger the return investors require as compensation for bearing that risk. Rate of return is what we earn from investment stated in percentage terms Higher risk means less certainty.

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Different Quantitative  Measures of Return
Holding Period Returns Holding period return comprises two components: 1. Capital appreciation 2. Income •. Capital appreciation : •. Income component of a return (RI): •. Total holding period return is simply = = 1 0 CA 0 0 CapitalAppreciation P -P P R = InitialPrice P P R I = Cash Flow InitialPrice = CF 1 P 0 R T = R CA +R I = P P 0 + CF 1 P 0 = P+CF 1 P 0 .

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Expected Returns Expected value represents the sum of products of possible outcomes, and probabilities that those outcomes will be realised. Expected return, E(RAsset), is an average of possible returns from an investment, where each of these returns is weighted by the probability that it will occur: If each of the possible outcomes is equally likely (that is, p1 = p2 = p3 = … = pn = p = 1/n), this formula reduces to: (7.2) E R Asset ( 29 = p i × R i ( 29 i = 1 n = p 1 × R 1 ( 29 + p 2 × R 2 ( 29 + .... + p n × R n ( 29 E R Asset ( 29 = R i ( 29 i = 1 n n = R 1 +R 2 +...+R n n
Slide 7 e.g. Holding period returns Jack purchased a share for \$45 one year ago. The share is now worth \$55. During the year, the share paid a dividend of \$1.25. What is the total return to Jack from owning the share? 1 0 1 1 0 0 55 45 1.25 11.25 0.25 25% 45 45 - + + = = - + = = = = P P CF P CF R T P P R T

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e.g. Expected Return -  probabilities If the return distribution for the asset is described as per table, what is the asset's expected return? Sli e Return Probability 0.10 0.25 0.20 0.50 0.25 0.25 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 2 2 1 0 25 10 0 5 20 0 25 25 2 5 10 6 25 18 75 = = × = × + × + + × = × + × + × = + + = .... . . . . . . % n Asset i i n n i Asset Asset E R p R p R p R p R E R E R
e.g. Expected Return – equal  weights Sli e The last four years of returns are as follows: What is the average annual return? 1 2 3 4 – 4% 28% 12% 4% ( 29 ( 29 ( 29 1 1 2 4% 28% 12% 4% 10% 4 ... = - + + + = = + + + = = n i i n Asset Asset R R R R E R n n E R

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Measure of Risk
Variance and standard deviation as measures of risk Calculating the variance and standard deviation The variance (2) 1. squares the difference between each possible occurrence and the mean (squaring the differences makes all the numbers positive) 3. multiplies each difference by its associated probability before summing them up: Var (R) = σ R 2 = p i × R i - E R ( 29 2 i = 1 n

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Variance and standard deviation as measures of risk Calculating the variance and standard deviation If all possible outcomes are equally likely, the formula becomes: Take the square root of the variance to get the standard deviation  (s ).
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