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Unformatted text preview: Risk and Return I Inflation Defined ♦ Inflation is an increase in the general price level. The general price level is periodically measured from a standard basket of goods. The Inflation Rate is the annual percent change in the price level. The most often quoted inflation measure is the rate of change in the Consumer Price Index. Real and Nominal Returns ♦ The Inflation rate: i The annual percent increase in the price level. ♦ Nominal Interest Rate: R The interest rate paid on debt securities without an adjustment for any loss in purchasing power. ♦ Real Interest Rate: r The nominal rate of interest less any loss in purchasing power of the dollar during the time of the investment. Real and Nominal Returns ♦ Nominal and real interest rates are related by: ♦ The last term, ir , is relatively small and is sometimes ignored for an approximate relationship: R ≈ i + r ( 29 ( 29 ir r i R r i R + + = + + = + 1 1 1 Real and Nominal Returns: Example ♦ Your stock portfolio earned 10.5% over the last year. If the rate of inflation last year was 3.1%, then what real rate of return did you earn? ( 29 ( 29 ( 29 ( 29 % 18 . 7 0718 . 1 1 031 . 1 105 . 1 1 1 1 1 = = + = + + + = + r r r i R r Measuring Returns ♦ We measure the growth rate in the value of an asset by computing the Holding Period Return: ♦ We can then average a series of returns over time using either an arithmetic average or a geometric average . Price Beginning Dividends Price Beginning Price Ending HPR + = Measuring Returns ♦ An arithmetic average is computed as ♦ A geometric average is computed as ∑ = = n i i A R n R 1 1 ( 29 1 1 1 1 + = ∏ = n n i i G R R HPR: An Example ♦ Suppose you bought IBM stock last month for $54.00 and were just paid a dividend of $1.00. Further suppose IBM stock is selling for $54.50 today. What is your return on IBM? % 78 . 2 00 . 54 00 . 1 00 . 54 50 . 54 1 1 = + = + = IBM t t t t IBM R P D P P R HPR: Another Example ♦ Suppose we observe the following series of weekly prices for ABIT Corp.: $96, $97, $101, $98 ♦ What are the weekly HPRs? 0297 . 101 101 98 0412 . 97 97 101 0104 . 96 96 97 3 2 1 = = = = = = HPR HPR HPR Averages ♦ What is the arithmetic average of the three HPRs? ♦ What is the geometric average? ( 29 ( 29 ( 29 [ ] 0069 . 1 0297 . 1 0412 . 1 0104 . 1 3 1 = × + × + = G R 0073 . 3 0297 . 0412 . 0104 . = + = A R Annualization ♦ Convert the arithmetic average weekly return into an APR ♦ Convert the arithmetic average weekly return into an EAR assuming weekly compounding. 37.96% or 3796 . 52 0073 . = × = APR ( 29 45.97% or 4597 . 1 0073 . 1 52 = = EAR Variance ♦ What is the variance of weekly ABIT returns?...
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 Spring '09
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 Capital Asset Pricing Model, Modern portfolio theory, Ri, The Market Portfolio

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