RISK & RETURN

FINANCIAL MANAGEMENTS.KHATUA

RISK & RETURN• Return--- 2 types• 1. Realized Return– Ex-Post( after the fact) return, return that

as/could have been earned.• Ex.- A deposit of Rs.1000 in a bank on 1/1, at a stated annual interest

rate of 10% will be worth Rs. 1100 exactly a year later.• 2.Expected Return– This is the return from an amount that investors

anticipate or expect to earn over some future period.• Components of return– 1.periodic cash receipts/income in the form of

dividend/interest etc.• 2.Appreciation/depreciation in the price of asset– capital gain/loss• Measuring rate of return (k) Dt + ( Pt -- Pt-1) k = -------------------- Pt-1

Examples• Ex.- If a share of ACC is purchased for Rs.3580 on 8th feb’04

& sold for Rs. 3800 on 9th feb’05 & the company paid a dividend for Rs. 35 for year, how do we calculate rate of return?

rate of return = 35 + (3800– 3580) 3580 = 0.713 or 7.13% Rate of Return of a Bond/ Debenture• Ex.- If a 14%, Rs.1000 ICICI debenture was purchased for

Rs.1350 & the price of this security rises to Rs. 1500 by the end of an year.

rate of return = 140 + 1500--1350 = 21.48% 1350

Expected Rate of Return

• A probability is a no. that describes the chances of an event taking place.

• 5 rules: 1. A prob. Can never be larger than 1. 2. Sum total of all prob. must be equal to 1. 3. Prob. Can’t be a negative no. 4. It’s range is 0 to 1. 5. Possible outcomes must be mutually exclusive• Expected rate of return for any asset is weighted

average rate of return using probability of each rate of return as the weight.

Examplerate of return = k= piki

Possible outcome (i)

Probabilities (pi) Rate of return(ki)

piki

1 0.1 0.5 or 50% 0.05

2 0.2 0.3 or 30% 0.06

3 0.4 0.1 or 10% 0.04

4 0.2 -.1 or -10% -0.02

5 0.1 -.3 or -30% -0.03

Total 1.0 K= 0.1 or 10 %

RISK

• Risk & Return go hand in hand in investment & finance• There is always a trade-off between risk & return• More risk & more return & vice versa• Risk is the chance the actual outcome from an

investment will differ from expected outcome• Broader the range of possible outcome, greater the risk• Variance or Std. Deviation can be a measure of risk• Variance: VAR(K) = pi ( ki – kexp)2

• Std. Deviation = = Sq. root of VAR(k)= [pi ( ki– kexp)2]1/2

Example

Possible outcome

Ki in %

(return)

Ki-- kexp ( ki – kexp)2 pi pi( ki – kexp)2

1 50 40 1600 0.1 1602 30 20 400 0.2 803 10 0 0 0.4 04 -10 -20 400 0.2 805 -30 -40 1600 0.1 160total Kexp=10%

= piki

1.0 VAR(K)=480

Std. Deviation= = 21.9%

SOURCES OF RISK

• Interest Rate Risk

• Market Risk

• Inflation Risk

• Business Risk

• Financial Risk

• Liquidity Risk

Example Economic Condition

• The stock of Alpha Co. performs well relative to other stocks during recessionary periods. The stock of Beta Co., on the other hand, does well during growth periods. Both the stocks are currently selling for Rs. 50 per share.

Calculate the exp. Return & Std. deviation of

1. Rs.1000 in equity stock of Alpha2. Rs.1000 in equity stock of Beta3. Rs.500 in each of equity stock

Alpha & Beta4. Rs.700 in Alpha & Rs.300 in BetaWhich of above 4 options would you

choose? Why?

Highgrowth

LG stagnation

recession

Prob 0.3 0.3 0.2 0.2

K(alpha) %

55 50 60 70

K(Beta) %

75 65 50 40