FIN2004 JAN17 Tutorial 3 Risk and Return I.pdf - Tutorial 3 Risk and Return I Conducted by Mr Chong Lock Kuah CFA 0 Key Points The average rate of

FIN2004 JAN17 Tutorial 3 Risk and Return I.pdf - Tutorial 3...

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0 Tutorial 3 : Risk and Return I Conducted by : Mr Chong Lock Kuah, CFA
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1 Key Points The average rate of return on a single risky asset from historical data is : The Geometric average return or geometric mean rate of return, (GM) on a single risky asset from historical data is : n R ...... R R R n R R n 3 2 1 n 1 t t 1 1/n n 3 2 1 ) R ) ..... (1 R )(1 R )(1 R (1 GM
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2 Which to Use? Consider the following investment : Year Beginning Value Ending Value Return (%) 1 $50.0 $100.0 100% 2 $100.0 $50.0 - 50% We can calculate the arithmetic mean rate of return (AM) as follows : AM = 1.0 + ( 0.5) 2 = 0.25 = 25% Note that we started with $50 and ended with exactly the same amount at the end of 2 years. The investment brought no change in wealth and therefore no return. Yet, the AM computes a mean return of 25% !
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3 Cont’d From the previous data Year Beginning Value Ending Value Return (%) 1 $50.0 $100.0 100% 2 $100.0 $50.0 - 50% We can calculate the geometric mean rate of return (GM) as follows : GM = { [ 1 + r 1 )( 1 + r 2 ) …….. ] 1/n 1 } x 100 GM = { [ 1 + 1 )( 1 0.5 ) ] 1/2 1 } x 100 = 0 Note that GM accurately measures that the investment has not yielded any return. So which is correct, 0 percent or 25 percent? Both are correct : They just answer different questions.
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