CHAPTER 1

Portfolio ManagementCHAPTER 7What are we going to learn in this chapter?Risk AversionYou have two stocks you consider for purchase; which one do you pick? Why?

50 TL certain 100/0 coin flip example

Risk averseRisk neutralRisk seeking

Main assumption about risk aversionMarkowitz Portfolio TheoryVariance of returns and diversification

The Markowitz model is based on several assumptions regarding investor behavior:1. Investors consider each investment alternative as being represented by a probability distribution of expected returns over some holding period.2. Investors maximize one-period expected utility, and their utility curves demonstrate diminishing marginal utility of wealth.3. Investors estimate the risk of the portfolio on the basis of the variability of expected returns.4. Investors base decisions solely on expected return and risk.5. For a given risk level, investors prefer higher returns to lower returns. Similarly, for a given level of expected return, investors prefer less risk to more risk.Alternative Risk MeasuresVariance & standard deviation of expected returns

Range of returns

SemivarianceExpected Rates of ReturnThe expected rate of return for an individual investment

What is the expected return for Tortu?

ProbabilityPossible Return RateExpected Return0.250.080.250.100.250.120.250.14E(R) =Expected Rates of ReturnThe expected rate of return for a portfolio of risky assets

What is the expected return for a portfolio of Sta, Arelik, Merko, Penguan Gda?

WeightExpected Sec. Ret.Expected Return0.200.100.300.110.300.120.200.13E(R) =RiskStandard deviation of returns for an individual investment

What is the standard deviation for Tortu?Possible Return RateExpected ReturnRi E(Ri)[Ri E(Ri)]^2

Pi([Ri E(Ri)]^2) * Pi

0.080.100.120.14RiskStandard deviation of returns for a portfolio of risky assets

Covariance

CorrelationCovarianceWhat is Covariance?

Prices vs. returns?

A positive covariance means .

A negative covariance indicates

The magnitude of the covariance depends on

CovarianceDateClose PriceDividendReturn R.Close PriceDividendReturn R.Dec 201160.938???45.688???Jan 201258.000???48.200???Feb 201253.030???42.500???Mar 201245.1600.18???43.1000.04???Apr 201246.1902.2847.1009.28May 201247.4002.6249.2904.65Jun 201245.0000.18-4.6847.2400.04-4.08Jul 201244.600-0.8950.3706.63Aug 201248.6709.1345.9500.04-8.70Sept 201246.8500.18-3.3738.370-16.50Oct 201247.8802.2038.230-0.36Nov 201246.9600.18-1.5546.6500.0522.16Dec 201247.1500.4051.0109.35Tuka & nye imento: E(R)=?Covariance

Covariance

CovarianceAlthough the rates of return for the two stocks moved together during some months, in other months they moved in opposite directions. The covariance statistic provides an absolute measure of how they moved together over time.

Formulation

Formulation for 12 monthly returns of 2 assets

When would covariation be positive/negative?CovarianceDateRiRjRi E(Ri)Rj E(Rj)[Ri E(Ri)] [Rj E(Rj)]Jan 2012-4.825.50?????????Feb 2012-8.57-11.83?????????Mar 201214.501.51?????????Apr 20122.289.284.097.8131.98May 20122.624.654.433.1814.11Jun 2012-4.68-4.08-2.87-5.5415.92Jul 2012-0.896.630.925.164.76Aug 20129.13-8.7010.94-10.16-111.16Sept 2012-3.37-16.50-1.56-17.9627.97Oct 20122.20-0.364.01-1.83-7.35Nov 2012-1.5522.160.2720.695.52Dec 20120.409.352.227.8817.47Tuka & nye imento: Covariance?Covariance & CorrelationWhat does the covariance figure mean?

Standardization

Correlation

Correlation boundaries and the interpretationCorrelationDateRi E(Ri)[Ri E(Ri)]^2Rj E(Rj)[Rj E(Rj)]^2Jan 2012-3.01???4.03???Feb 2012-6.76???-13.29???Mar 2012-12.69???0.04???Apr 20124.0916.757.8161.06May 20124.4319.643.1810.13Jun 2012-2.878.24-5.5430.74Jul 20120.920.855.1626.61Aug 201210.94119.64-10.16103.28Sept 2012-1.562.42-17.96322.67Oct 20124.0116.09-1.833.36Nov 20120.270.0720.69428.01Dec 20122.224.927.8862.08Tuka & nye imento: Correlation?Standard Deviation of a PortfolioWhat does the standard deviation of a portfolio indicate?

Formal formulationStandard Deviation of a PortfolioEXAMPLE:E(Ra) = 0.20 Stn. Dev. = 0.10 Wa = 0.50E(Rb) = 0.20 Stn. Dev. = 0.10 Wb = 0.50Correlation = 0.10Risk = ?

The lesson learnt?

Standard Deviation of a PortfolioEXAMPLE:E(Ra) = 0.20 Stn. Dev. = 0.10 Wa = 0.50E(Rb) = 0.20 Stn. Dev. = 0.10 Wb = 0.50Correlation = 0.05Risk = ?

The lesson learnt?

Standard Deviation of a PortfolioEXAMPLE:E(Ra) = 0.20 Stn. Dev. = 0.10 Wa = 0.50E(Rb) = 0.20 Stn. Dev. = 0.10 Wb = 0.50

If Correlation = 0.00Stn. Dev. ?

If Correlation = -0.50 Stn. Dev. ?

If Correlation = 0.00Stn. Dev. ?Standard Deviation of a PortfolioEXAMPLE:If Correlation is 1.00; what is the risk of the portfolio?AssetE(Ri)W(i)Variance(i)Stn. Dev. (i)10.100.500.0049???20.200.500.0100???Standard Deviation of a PortfolioWhat if the correlations were:+0.50 0.00 -0.50 -1.00Three Asset PortfolioCorrelations:r S,B = 0.25r S,C = -0.08r B,C = 0.15

Expected return = ?Standard deviation = ?Asset ClassesE(Ri)Stn. Dev. (i)Weight (i)Stocks0.120.200.60Bonds0.080.100.30Cash Equivalents0.040.030.10The Efficient FrontierIf we examined different two-asset combinations and derived the curves assuming all the possible weights, we would have a graph like:The Efficient Frontier

The Efficient FrontierEfficient frontier

Comparisons of portfolios A, B and C

As an investor, you will target a point along the efficient frontier based on your utility function and your attitude toward risk.

No portfolio on the efficient frontier can dominate any other portfolio on the efficient frontier. All of these portfolios have different return and risk measures, with expected rates of return that increase with higher risk.The Efficient Frontier

Efficient Frontier & Investor UtilitySlope of the efficient frontier

An individual investors utility curves

Two investors will choose the same portfolio from the efficient set only if their utility curves are identical.

The optimal portfolioEfficient Frontier & Investor Utility

END OF CHAPTER