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Lecture 1- Part 2

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Lecture 1- Part 2 Risk Management and Derivative by Stulz, Ch:2 Expected Return and Volatility A key measure of investors success is the rate at which their funds ... – PowerPoint PPT presentation

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Title: Lecture 1- Part 2


1
Lecture 1- Part 2
  • Risk Management and Derivative by Stulz, Ch2
  • Expected Return and Volatility

2
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

3
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

4
  • 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

5
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) SRiPi

6
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
7
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 SRi-E(R)2 Pi

8
Variance of Returns (Risk)
  • Standard Deviation taking square root of
    .00600, we get value of 0.077 or 7.7

Return Probability RiPi Ri-E(R) SRi-E(R)2 SRi-E(R)2 Pi
0.10 0.30 0.03 -.03 .0009 .00027
0.2 0.50 .1 .07 .0049 .00245
0 0.20 0 -.13 .0169 .00338
Sum .13 .00600
9
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

10
Cumulative Distribution Function
11
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

12
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

13
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) Swi E(Ri)
  • Wi Weight of the security in the poftfolio
  • E(Rp) The expected return on the portfolio

14
Calculating portfolio return
  • Calculating weights PPL 20000/60000 .33
  • FFC 30000/6000 .5 Lucky 10000/60000
    .16

Stock Value Return Weight Swi E(Ri
PPL 20000 15 .33 4.95
FFC 30000 12 .5 6
Lucky 10000 10 .16 1.6
Sum 12.55
15
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

16
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

17
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

18
Efficient Frontier
  • 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
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