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

• 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

Formula of Calculating RR

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.

Example,,,

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.

Period Returns1 15 %2 30%3 -12%Total 33%Arithmetic Mean

33/3 = 11%

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 – 1GM = [(1.15)(1.30)(0.88)] 1/3 – 1GM = 1.096 – 1GM = 0.096 or 9.6%

Problem with Arithmetic Mean

Period Opening Ending Change

1 20 40 40-20/20 = 1 or 100%

2 40 20 20-40/40 = -0.5 or -50%

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%.

Use of Geometric Mean