Lecture 4.Ppt

Portfolio Construction

Markowitz Portfolio SelectionMarkowitz provided a comprehensive framework for analysis of portfolio

Portfolio of securities is an integrated whole, each securities complementing the other Consider both the characteristics of individual security and the relationship between these securities.Investors like return and dislike risk


Find the set of portfolio that Provides the minimum risk for every possible level of return.The Efficient SetInvestor select from the efficient set that meets his/her requirements


Maximize the expected returnMinimize the variance

Portfolio ConstructionMinimize portfolio Risk

Portfolio ConstructionSubject to:A Stated Expected Return


Covariance measures the extent to which two securities tend to move, or not move, together.

The variance of an individual security is the sum of the probability-weighted average of the squared differences between the securitys expected return and its possible returns.

The standard deviation is the square root of the variance. Both variance and standard deviation measure of total risk.


Correlation Co-efficientA correlation of +1.0 would indicate perfect positive correlation, and a value of 1.0 would mean that the returns moved in a completely opposite direction. A value of zero would mean that the returns had no linear relationship, that is, they were uncorrelated statistically.


Probability Possible Returns0.1 0.20

0.15 0.050.2 0.1

0.25 0.150.2 0.20.1 0.4

Considering the world economic outlook for the coming year and estimates of sales and earnings for the pharmaceutical industry, you expect the rate of return for Lauren Labs common stock to range between 20 percent and +40 percent with the following probabilities:

Compute the expected rate of return [E(Ri)] for Lauren Labs.


[E(Ri)] for Lauren Labs

Possible ExpectedProbability Returns Return0.10 -0.20 -0.02000.15 -0.05 -0.00750.20 0.10 0.02000.25 0.15 0.03750.20 0.20 0.04000.10 0.40 0.0400

E(Ri) = 0.1100


Stock Market Value ($ Mil.) E(Ri)Morgan Stanley $15,000 0.14Starbucks 17,000 0.04General Electric 32,000 0.18Intel 23,000 0.16Walgreens 7,000 0.12

Given the following market values of stocks in your portfolio and their expected rates of return, what is the expected rate of return for your common stock portfolio?


Market Weight SecurityPortfolio Return

Stock Value (Wi) Return (Ri) Wi x RiMorgan $15,000 0.16 0.14 0.0224

Starbucks 17,000 0.18 -0.04 -0.0072GE 32,000 0.34 0.18 0.0612Intel 23,000 0.24 0.16 0.0384

Walgreens 7,000 0.08 0.05 0.004

$94,000 E(Rport) = 0.1188


The standard deviation of Shamrock Corp. stock is 19 percent. The standard deviation of Baron Co. stock is 14 percent. The covariance between these two stocks is 100. What is the correlation between Shamrock and Baron stock?


Given the following information:Standard Deviation for the Stock X = 12%Standard Deviation for the Stock y = 20%Expected return for the stock X =16%Expected return for stock Y = 22%Correlation coefficient between X and Y = 0.30

Calculate Covariance between X and Y


Calculate the number of covariances needed for an evaluation of 500 securities

a.using the Markowitz model. b.using the Sharpe model

Portfolio ConstructionThe number of unique covariances needed for 500 securities using the Markowitz model is: n(n-1) 500(499) 249,500 = = = 124,750 2 2 2

The number of covariances needed for 500 securities with the Sharpe model is 500.


The expected return for the market is 12 percent, with a standard deviation of 20 percent. The expected risk free rate is 8 percent. Information is available for five mutual funds, all assumed to be efficient, as follows:

Mutual Funds SD%

Affiliated 14

Omega 16

Ivy 21

Value Line Fund 25

New Horizon 30


Calculate the slope of CMLCalculate the expected return for each portfolioRank the portfolio in the increasing order of expected returnDo any of the portfolio have the same expected return as the market? Why

Portfolio Construction(a) CML slope = (12-8)/20 = .2 (b) Affiliated 8 + .2 (14) = 10.8%

Omega 8 + .2 (16) = 11.2%Ivy 8 + .2 (20) = 12.0% Value Line 8 + .2 (25) = 13.0%New Horizons 8 + .2 (30) = 14.0%

(c) The rank order is the same as in (b), which is from low risk to high risk. (d) Ivy does because it has the same risk as measured by the standard deviation.


Expected Return and Standard Deviation of Two stocks is given below

E(R1) = 0.201 = 0.10E(R2) = 0.202 = 0.10Both the assets have equal weight i.e. (W1 = 0.50; W2 = 0.50).

Portfolio ConstructionCorrelation co-efficient between Stock 1 and 2 is as follows:

a. r1,2 = 1b. r1,2 = 0.50C. r1,2 = 0.00d. r1,2 = -0.50e. r1,2 = -1Calculate Portfolio Risk under all the five conditions


Both the assets have equal weight i.e. (W1 = 0.50; W2 = 0.50).

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You are considering two assets with the following characteristics: E(R1) = .15 E(R2) = .20

1 = .10 W1 = .52 = .20 W2 = .5 Compute the mean and standard deviation of two portfolios if r1,2 = 0.40 and 0.60, respectively.

Portfolio ConstructionGiven: E(R1) 0.10

E(R2) 0.151 = .032 = .05

Calculate the expected returns and expected standard deviations of a two-stock portfolio in which Stock 1 has a weight of 60 percent under the following conditions: a. r1,2 = 1.00b. r1,2 = 0.75c. r1,2 = 0.25d. r1,2 = 0.00e. r1,2 = 0.25f. r1,2 = 0.75g. r1,2 = 1.00

Portfolio ConstructionGiven the following information:Standard Deviation for the Stock X = 12%Standard Deviation for the Stock y = 20%Expected return for the stock k X =16%Expected return for stock Y = 22%Correlation coefficient between X and Y = +1.0Choose the investment below that represent the minimum risk portfolio100 investment in stock Y100% investment in stock X50% investment in stock X and 50% investment in Stock Y80% investment in stock Y and 20% investment tin stock X

Portfolio ConstructionYou are a UK-based investor evaluating the effect upon your domestic equity portfolio of allocating 25% of assets to the newly independent Republic of Turkmanistan. Turkmanistan is an emerging market and you believe expected returns from investment there will average 20% per year for the foreseeable future. You also expect substantial volatility, up to 30% in annual standard deviation of returns. Countering this risk, however, is your belief that the fortunes of Turkmanistan are only modestly correlated with those of the UK, and you estimate the correlation coefficient to be only 0.25. If domestic equity shares are expected to return 10% annually, with 15% annual standard deviation of returns, what is the expected return and risk for a portfolio combining 75% domestic equity and 25% shares from Turkmanistan?

Lecture 4.Ppt

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