Risk and Return

Rates of Return
 A key measure of investors’ success is the
rate at which their funds have grown
 Holding-period return (HPR) of shares is
composed of capital gain and dividend
 RH = (C)+ (PE-PB) /PB
 This definition assumes end of period returns
and ignores re-investment of income

 Return Relative It is a different way to
calculate return. This method is used when a
cumulative wealth index or a geometric mean
has to be calculated.
Return Relative (RR)= C+PE/PB
Rates of Return

Rates of Return
 Dividend Yield = Percentage return from
dividends i.e. (D/PB)x100
 To calculate HPR over a period of time, we
can use:
 Arithmetic average
 Geometric average
 Dollar weighted return

Arithmetic Average
 It is the sum of periodic return divided by number of
periods
 Arithmetic Average = 15/3 = 5%
Period 1 10%
Period 2 25%
Period 3 -20%
Sum 15%

Geometric Average
nth root of the product of returns for n years
Geometric mean = (1+R1)x(1+R2)x(1+R3)1/n
– 1
 = [(1+10%) x (1+ 25%) x(1+(-20%))] 1/3
– 1
 [(1.1) x (1.25) x (.8)] 1/3
– 1
 (1.1) 1/3
– 1
 1.03-1
 .03 or 3%

Problem with Arithmetic
average
 Suppose the following:
 Calculating arithmetic mean gives false value of 25% return =
(100%-50%)/2
 And geometric = (1+1)x(1-.5)1/2
- 1
 =1-1 = 0%
Year Begin
value
Ending
value
HPR
2007 50 100 100%
2008 100 50 -50%

Geometric Vs Arithmetic
 In highly volatile security prices, arithmetic
mean is biased upward and we should use
geometric mean
 If rates of returns are the same for all years,
geometric and arithmetic averages gives
same results

Taking a Global
 When investors buy or sell securities in other
countries, they also take exchange rate risk
or currency risk
 Fluctuation in currency value can be either a
source of loss or profit
 If the foreign currency strengthens, your
returns will increase or vice versa

An Example
 Suppose you purchased 100 shares of IBM at NYSE for
$300 each. The dollar-rupee parity was 60 rupees a
dollar at the that time. So your total investment in rupees
was 100x$300 = $30000 x 60 =Rs.1800,000
 At the end of the year, IBM share price was $310, giving
you $10 profit per share, your profit is = 100 x 10 =
$1000x60 = Rs.60000
 But the dollar-rupee parity had jumped to 78 rupee a
dollar, now your total investment is =100x310 = $31000
x 78 = Rs.2418000
 And your profit is 2,418,000-180,0000 = Rs.618,000
 Or in percentage = 618,000/1800,000 = .343 or 34%

Equation for calculating
returns from foregin stocks
 = [(P1/Po)x(C1/Co)] – 1
 [(310/300)x(78/60)] – 1
 [(1.03) x (1.3)] – 1
 1.339 – 1
 0.339 or 34%
 P1 = Ending share price
 Po = Beginning share price
 C1 = Ending value of domestic currency
 Co = Beginning value of domestic currency

Risk
 Any investment involves some degree of
uncertainty about future returns
 Risk arises out of variability in returns
 If an asset has no variability in returns, the
assets is considered to be risk free like one
year T-bills

Type of Risk
Systematic Risk (Not diversifiable)
 Market Risk
 Interest Rate Risk
 Purchasing Power Risk
Unsystematic Risks (Diversifiable)
 Business Risk
 Financial risk

Sources of Risk
 Market risk : variability in returns due to
fluctuations in aggregate market
 Recession, wars etc
 Interest Rate Risk
Interest risk refers to variability of total returns,
particularly on fixed income securities due fluctuation in
Interest rates.
 Purchas Power or Inflation risk
 when purchasing power declines.
 Inflation also leads to hike in interest rates because
lenders demand more to compensate themselves for
loss in purchasing power

 Exchange risk = for international investors,
a source of risk come from exchange rate
fluctuation
 Country Risk = For international investors,
economic and political stability, law and order
situation are important consideration in the
investment decision
Sources of Risk

Interest rates and returns
 1. Increase in interest rates increases the
required rate of return
 RRR= Rf + Risk premium which reduces the
prices of the securities (intrinsic value)
 2. It increases cost of borrowing and hence cost
of capital
 3. It reduces money supply which lower demand
for securities and resultantly prices fall.
RRR
Cashflow
alueIntrinsicV
+
=
1

Measuring Risk
 The most commonly used measure of risk
for securities is standard deviation
 SD measure the total risk of a security or a
portfolio
 It measure deviations of each observation
from the arithmetic mean
1
]R-[R
1
2
_
i
−
=
∑=
n
n
i
σ
Measuring Risk

Standard Deviation
89.5
4
139
15
139
==
−
1
]R-[R
1
2
_
i
−
∑=
n
n
i

Interpretation
 The 5.89 SD means that the security return
can fluctuate between +/-5.89 from the mean
value of 16%
 More specifically, the return can fluctuate
between 16 - 5.89 = 10.11 or 16 + 5.89 =
21.89
Your return could fall to as low as
10.11% or could rise to 21.89 %

Realized Returns and risk
from Investing
Class of assets Average SD
S&P 500 Composite 9.21% 19.75%
S&P Industrial 9.66 21.57
S&P Utility 8.47 20.54
Small Cap Stock (S&P 600) 14.82 37.23
AAA 20-year Corp Bond 3.87 10.05
US 15-year Bond 3.25 10.22
T-Bills 1.569 4.65

Risk and Return

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Risk and Return