EXPECTED RETURN PORTFOLIO Pertemuan 8 Matakuliah: F Analisis Kuantitatif Tahun: 2009

What is a “Portfolio?” A portfolio is a list of securities indicating how much is (or will be) invested in each one; The question is: which portfolio should be selected?

7.2 The Return on a Portfolio You have funds W 0 to invest in a portfolio at the beginning of the period; By definition we have W 1 = W 0 (1 + r p ), where r p is the return on your portfolio; But at time 0, you do not know what W 1 will be for any given portfolio because you do not know what r p will be for that portfolio; At time 1 you know what is W 1 ; Hence, r p is a random variable ex ante but is known ex post. Bina Nusantara University 3

How Should You Evaluate Alternative Portfolios? What is the “good thing” you want from your portfolio? Return. You want “return to be high;” What is the “bad thing” you want to avoid in your your portfolio? Risk. You want “risk to be low;” Hence, how should you evaluate alternative portfolios? By examining their expected returns and their standard deviations. Observe, therefore, that you have two conflicting objectives: (1) maximize the expected return on your portfolio; and (2) minimize the standard deviation of your portfolio.

7-4 Harry Markowitz and his paper “Portfolio Selection” [Journal of Finance (1952)] are generally viewed as the origin of modern portfolio theory. He was awarded the 1990 Nobel Prize with William Sharpe and Merton Miller for their pioneering work in the theory of financial economics. 7.4 Calculating the Expected Return of a Portfolio The expected return on a portfolio is the weighted average of the expected returns on the securities included in that portfolio; What is the weight of a security in a portfolio? It is the percentage of wealth invested in that security;

7-5 The formula to compute the expected return on a portfolio of N securities is where is the expected return on security i. is the weight of security i; and

7-6 Example On January 25, 1999, you bought the following stocks: You expect to earn the following (annual) returns on the stocks you bought: 20% on Microsoft, 12% on IBM, and 15% on Coca-Cola. What is the expected return on your portfolio? Table 7.1

7-7 First, we need to compute the weight of each security. The total wealth invested is equal to W 0 =($171*200) + ($ *500)+($62.50*1,000) =$34,200+$92, $62,500 =$189, Hence, X 1 =18.05%[=$34,200/$189,512.50]; X 2 =48.97%[= $92, /$189,512.50]; X 3 =32.98%[= $62,500 /$189,512.50]. [Note that X 3 = 1-X 1 -X 2 ]

Bina Nusantara University 9 EXPECTED RETURN OF PORTFOLIO Most investors do not hold stocks in isolation. Instead, they choose to hold a portfolio of several stocks. When this is the case, a portion of an individual stock's risk can be eliminated, i.e., diversified away. This principle is presented on the Diversification page. First, the computation of the expected return, variance, and standard deviation of a portfolio must be illustrated. Diversification

Bina Nusantara University 10 StateProbability Return on Stock A Return on Stock B 120%5%50% 230%10%30% 3 15%10% 320% -10% Once again, we will be using the probability distribution for the returns on stocks A and B. From the Expected Return and Measures of Risk pages we know that the expected return on Stock A is 12.5%, the expected return on Stock B is 20%, the variance on Stock A is.00263, the variance on Stock B is.04200, the standard deviation on Stock S is 5.12%, and the standard deviation on Stock B is 20.49%.Expected ReturnMeasures of Risk Once again, we will be using the probability distribution for the returns on stocks A and B.

Bina Nusantara University 11 Portfolio Expected Return The Expected Return on a Portfolio is computed as the weighted average of the expected returns on the stocks which comprise the portfolio. The weights reflect the proportion of the portfolio invested in the stocks. This can be expressed as follows: where E[R p ] = the expected return on the portfolio, N = the number of stocks in the portfolio, w i = the proportion of the portfolio invested in stock i, and E[R i ] = the expected return on stock i. For a portfolio consisting of two assets, the above equation can be expressed as

Bina Nusantara University 12 For a portfolio consisting of two assets, the above equation can be expressed as

Bina Nusantara University 13 Expected Return on a Portfolio of Stocks A and B Note: E[R A ] = 12.5% and E[R B ] = 20% Portfolio consisting of 50% Stock A and 50% Stock B Portfolio consisting of 75% Stock A and 25% Stock B