Page 40 of 46 4th July 2019 businessbusiness

Page 40 of 46 4th july 2019 businessbusiness

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Page 40 of 46 4th July 2019 - risk/content-section-0
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Investment risk Activity 1 Answer You probably found that most people preferred Investment A, but what sort of reasons did you and they give? One answer is something like this. The benefit conferred by the unexpected extra income of, say, £a in a good year is somehow less than the corresponding pain inflicted by the unexpected shortfall of £a in a bad year. This could be because, as our income increases, we spend each marginal pound on less essential goods and services. On average, for every good year when Investment B produces a return of (x + a)%, there will be a correspondingly bad year when it produces a return of only (x – a)%. In the terminology of economics, the extra a% earned in the good year gives the investor less utility than is lost by the shortfall of a% in the bad year. So the total utility of the fluctuating returns on B will be less than the total utility of the constant return on A. Most investors will therefore prefer Investment A. Back to Session 1 Activity 1 Page 41 of 46 4th July 2019 - risk/content-section-0
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Investment risk Self-assessment question 1 Answer 1. T ot al re tu r n ( % p er a n n u m ) Fre qu en cy of occ urr en ce Pr ob abi lity Pr ob abi lity - we igh ted ret ur n (% pe r an nu m) −7 4 0.04 −0.2 8 3 15 0.15 0.45 10 18 0.18 1.80 15 24 0.24 3.60 21 19 0.19 3.99 26 12 0.12 3.12 29 8 0.08 2.32 T ot al / M e a 10 0 15. 00 % Page 42 of 46 4th July 2019 - risk/content-section-0
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Investment risk n 2. The main assumption that you made was that the future can be extrapolated from the past. You may well take the view that demand for this particular company's product is unlikely to fluctuate substantially over time! 3. A n n u al re tu r n R I Dis pe rsi on E (R ) − R i Sq ua re of dis pe rsi on [ E( R) − R I ] 2 Pr ob abi lity P I P i [ E(R ) − R i ] 2 −7 % 22 484 0.04 19.3 6 3 % 12 144 0.15 21.6 0 10 % 5 25 0.18 4.50 15 % 0 0 0.24 0 21 % −6 36 0.19 6.84 26 % −11 121 0.12 14.5 2 29 % −14 196 0.08 15.6 8 82. 50 Page 43 of 46 4th July 2019 - risk/content-section-0
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Investment risk Sum of the squares of the probability-weighted dispersions (= variance) Square root of variance (V) = standard deviation (S) = 82.50 = 9.083 4. The table shows a pattern quite close to a normal distribution. The mean and mode do coincide at 15.00%. There is a slight asymmetry in the shape of the ‘shoulders’ of the bell. The ‘tails’ at opposite ends of the distribution differ from each other slightly, but not so much as to skew the data significantly in one direction or the other. Overall, we can say that standard deviation is still a useful measure of dispersion for a table of this type.
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