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Risk and Return. Introduction. Investment has two aspects: Security Analysis and Portfolio Analysis Security analysis consists of valuation of financial assets. Value is the function of risk and return. Realized risk (ex-ante) and return and Expected Risk and return (ex-post). Return.
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Introduction • Investment has two aspects: Security Analysis and Portfolio Analysis • Security analysis consists of valuation of financial assets. • Value is the function of risk and return. • Realized risk (ex-ante) and return and Expected Risk and return (ex-post)
Return • Return is the reward of investment such as interest on bonds and dividend on shares. • Realized is historical return which already earned. • Two components of returns: • Yield: The income component of a security in the form of periodic interest or dividend. Yield • Capital Gains...
Capital Gain (loss): The change in price on a security over some period of time or • It is the appreciation (depreciation) in the price of the assets known as capital gain (loss) • The difference between purchase price and selling price
Total Return = Yield + Price Change (Capital gain & loss) • Where TR = Total Return; = Cash Flow during a period; = Ending Price of Security; = Beginning Price of Security
Return Relative (RR) • The total return for an investment for a given time period stated on the basis of 1.0 • It is used to eliminates negative numbers by adding 1.0 to the total return. • RR = TR in decimal form + 1.0 • TR in decimal form = RR - 1.0 • E.g., TR of 0.50 have RR of 1.50 and TR of -9.07% (-0.0907) the RR will be -0.0907+1 = 0.9093
Cumulative Wealth Index (CWI) • It measures how one’s wealth in rupee changes over time. • So it is the accumulation of wealth of series of returns over period. • It refers that how much Rs. 1 investment will generate returns over a period. • CWIn = WI0 (1+TR1) (1+TR2).........(1+TRn) OR • CWIn = WI0 (RR1) (RR2).........(RRn) • Where, CWIn = Cumulative Wealth Index; WI0 = Initial Investment; TR = Total Returns; RR = Return Relative • TR is stated in percent or demical; RR on the basis of 1.0 and CW is stated in dollars
Taking a Global Perspective • While investing globally, investor has to look at the exchange risk (currency risk) • Exchange Risk is the adverse impact on the return as a result of fluctuation in currency rates. Or decrease of home currency relative to foreign currency. • The fluctuation in currency may be a source of profit and loss. • Increase in currency rate lead to profit and vice versa.
Formula of Calculating Currency-Adjusted Returns • TR = RR -1 • If the dividend is zero, then RR = (PE/PB) • TR = [(PE/PB) x(C1/C0)] – 1 • Where, • PE = Ending Share Price • PB = Beginning Share Price • C1 = Ending Value of Domestic Currency • C0= Beginning Value of Domestic Currency
Statistics for Returns • Taking the average of series of returns need to be averaged. • Two methods of calculating average • Arithmetic Mean • Geometric Mean
Arithmetic Mean • The sum of periodic returns divided by number of periods.
Geometric Mean Geometric mean is the nth root of the product of returns for n years. Geometric mean = (1+R1)x(1+R2)x(1+R3)1/n – 1 GM = [(1+ 15%) x (1+30%) x (1+ (-12))]1/3 – 1 GM = [(1.15)(1.30)(0.88)] 1/3 – 1 GM = 1.096 – 1 GM = 0.096 or 9.6%
Problem with Arithmetic Mean • Arithmetic Mean = 100 + (-50)/2 • A M = 25% • Geometric Mean = [(1+1)(1-0.5)] 1/2 – 1 • GM = 1 – 1 • GM = 0% • The Arithmetic Mean gives a false value of 25%.
