Transcript Lecture 1

Lecture 1- Part 2
Risk Management and Derivative by
Stulz, Ch:2
Expected Return and Volatility
Knowing risk and return of securities
and portfolios
• 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
• HPR = (P1-Po + Cash Dividend)/Po
• This definition assumes end of period returns
and ignores re-investment of income
Return Distributions
• If the return on a stock is fixed, there will be
100% probability (Certaininty)that the return
will be realized, like in bonds and T-bills
• In stocks, return is not fixed so the probability
of all likely outcomes should be assessed
• Probability is the chance that the specified
outcome will occur
• Probability distribution is the specification of
likely outcomes and the probability associated
with each outcome
• Suppose we expect that PPL can give either
10%, 20% or -5% return. So we have three
possible outcomes, if we associate chances of
occurrence with each return, then it becomes
probability distribution
Expected Return
• Expected return is the single most likely
outcome from a PD
• It is calculated by taking a weighted average of
all possible return outcomes
• E(R) = ΣRiPi
An Example
Oil Prices Return
Probability RiPi
Flat
0.10
0.30
0.03
Rise
0.2
0.50
.1
Fall
0
0.20
0
Sum
.13
Variance of Returns (Risk)
• Variance of a random variable is a statistical
tools that measures how the realization of the
random variable are distribute around their
expected values
• In other words it measures risk
• Variance = Σ[Ri-E(R)]2 Pi
Variance of Returns (Risk)
Return Probab RiPi
ility
0.10
0.30
0.03
[Ri-E(R)]
Σ[Ri-E(R)]2
-.03
.0009
.00027
0.2
0.50
.1
.07
.0049
.00245
0
0.20
0
-.13
.0169
.00338
Sum
.13
Σ[Ri-E(R)]2
Pi
.00600
Standard Deviation: taking square root of .00600, we
get value of 0.077 or 7.7%
Cumulative Distribution Function
• The cumulative distribution function of a
random variable y specifies, for any number y,
the probability that the realization of the
random variable will be no greater than y
• For POL, a reasonable estimate of the stock
return volatility is 9.2% with expected return
of 13%, the following table show cumulative
distributions functions for different levels of
returns
Cumulative Distribution Function
Return
CDF
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0
0.00016728
0.006209665
0.07882147
0.372179283
0.776632511
0.967686247
0.998331093
0.999971115
0.999999838
CDF
1.2
1
0.8
0.6
0.4
CDF
0.2
0
-0.4
-0.2
0
0.2
0.4
0.6
0.8
How to Calculate CDF
• CDF can easily be calculated with MS Excel
• Put the equal sign in a cell =
• Open parenthesis and give x value (x means
the level of return for which you want
cumulative probability)
• Then give the mean return value,
• Then the standard deviation value
• And finally write TRUE and close parenthesis
Interpretation
• Taking values from the table in the previous
slide, CDF is .59 with the 20% return level
• It means that there is 59% probability that
return on POL will be less than 20%
• An investor has Rs.100,000 investment in POL
and he wants that he does not lose more than
Rs.30000 of his investment, what is the
probability of this occurrence
Return of a Portfolio
• To calculate an average rate on a combination
of stocks, we simply take the weighted
average return of all stocks
• E(Rp) = Σwi E(Ri)
• Wi = Weight of the security in the poftfolio
• E(Rp) = The expected return on the portfolio
Calculating portfolio return
Stock
PPL
FFC
Lucky
Sum
Value
20000
30000
10000
Return
15%
12
10
Weight
.33
.5
.16
Σwi E(Ri
4.95
6
1.6
12.55
• Calculating weights: PPL = 20000/60000 = .33
• [FFC = 30000/6000 = .5] [Lucky = 10000/60000 = .16
Calculating Portfolio Risk
• Risk of the porftolio is not the weighted average risk
of the individual securities
• Rather it is determined by three factors
– 1.the SD of each security
– 2. the covariance between the securities
– The weights of securities in the portfolio
 p  [ wA2 A2  wB2 B2  2wA wBCovAB ]1/ 2
OR
 p  [ wA2 A2  wB2 B2  2wA wB  AB A B ]1/ 2
Diversification
• By combining negatively correlated stocks, we can
remove the individual risks of the stocks
• Example: Pol face the risk of falling oil prices
• PIA face the risk of rising oil prices
• By combining these two stocks, reduction in return in
one stock due to change in oil price is compensated
by increase in return of the other stock
• However, all of market risk cannot be eliminated
through diversification
Efficient Frontier
• Investors should select portfolios on the basis of
expected return and risk
• A portfolio is efficient if:
– 1 it has the smallest level of risk for a given return or
– 2. largest return for a given level of risk
• To select efficient portfolios, investors should find
out all portfolios opportunities set
• i.e find out risk and return set for all portfolios
Efficient Frontier
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Example given in the Excel File
Steps:
1. Calculate securities return
2. calculate portfolio returns
3. Find portfolio risk
4. Make different portfolios by changing weights of the
securities
5. Find risk and return of each portfolio developed in step 4
6. Plot the risk and return of these portfolios
7. Find the minimum variance portfolio
8. Portfolios above the minimum variance portfolios are
efficient