Diversification, risk, return and the market portfolio

When we take risk we expect an equivalent return Investors can reduce their risk and also their expected return by investing in a combination of assets in different firms, industries and countries. This is called diversification. The limit of diversification is to invest in every possible asset in the world. This imaginary investment is called the market portfolio. Introduction

Diversification Market Portfolio Outline

Shipping routes Britain to Australia

Why would the same shipping company with the same products, leaving at the same time decide to take 2 different routes from Britain to Australia? They sent half of their ships around South Africa and half through the Suez canal. Question

Diversification can give reduced risk when we invest our money in different types of assets and firms. An important factor in measuring the benefit of diversification is correlation. Diversification

Correlation, in the world of finance, is a statistical measure of how two securities move in relation to each other. Correlation is measured using the correlation coefficient, which ranges between -1 and +1. Perfect positive correlation (a correlation co- efficient of +1) implies that as one security (security is a financial asset, such as a bond or a stock) moves, either up or down, the other security will move equally at the same time, in the same direction Correlation

In our example above if the storms generally happened at the same time on both routes or were correlated then there would not be much benefit from sending the ships on different routes. If when a storm was happening on one route there was no chance of a storm happening on the other route, or they were negatively correlated, this would give the highest benefits of diversification. Correlation

We can look at risk for stock prices as historical variance around expected returns. Variance around expected returns is a measure of the squared difference between the actual returns and the expected returns on an investment. Variance around expected returns

An investment in stock in an oil drilling firm If we looked at the historical data for the last 30 years and compared the expectation of investors at the start of the year with the actual performance of the stock price of the oil drilling firm we would see a difference every year. The stock price could go anywhere from - 90% to +150% depending on the year. High variance

An investment in a 10-year United States government bond is generally viewed as a riskless investment. If we look at the last 30 years there is no variance around expected returns. We always got exactly the same returns as we expected because the fixed payments were made in the correct amount and on time. No variance

Let’s say we have two stocks 1 and 2. The variance around expected returns for 1 is 10% and 2 is 20%. If both stocks are perfectly correlated (which would never happen in real life) and we invest 50% of our money in 1 and 50% of our money in 2 we can find the weighted average variance of the two stocks. Example

Portfolio variance = (weight1*variance1 + weight2*variance2).5(.1) +.5(.2) = =.15 or 15% Weighted average

In another case stocks 1 and 2 have a covariance of 0 or no relationship. From statistics we learn that the variance of two random variables is a function of the variance of each variable and the covariance between the variables. This relationship directly applies in calculating the variance of a two asset portfolio as follows: Example

Portfolio variance = (weight(1)^2*variance(1) + weight(2)^2*variance(2) + 2*weight(1)*weight(2)*covariance(1,2) (.5)^2(.1) + (.5)^2(.2) + 2(.5)(.5)(0) = =.75 or 7.5% Example

The portfolio which gives us the lowest portfolio variance would include every possible risky asset in the market. This portfolio of every traded risky asset in the market place is called the market portfolio. Market portfolio

Investors can decide on how much risk they would like to take by making some combination of an investment in a riskless asset like the US government bonds or in the market portfolio. For example Warren buffet suggests a 90% investment in an index fund following the Standard & Poor's 500 Index (S&P 500) and a 10% investment in short term US government bonds for his wife’s retirement fund. Market portfolio

We should note is that there is no reason that the market portfolio will perform better than the riskless investment. In finance we have to think about risk and return. We may expect a higher return by investing in the market portfolio but we are taking a risk of losing our money which does not exist in the riskless investment. Market portfolio

In theory over the long term it shouldn’t matter whether we invest in a riskless investment or the market portfolio. In the market portfolio some years we win and get more than the expected return, some years we lose and get less. It is simply our attitude to risk that causes us to choose one investment over another. Market portfolio

1.What is the benefit of diversification? 2.What is the market portfolio? 3. Which of the following investments would a risk adverse (doesn’t like risk) investor prefer? Why? A.A portfolio of two stocks both with variances of 10% where the correlation of the stocks is 0.9 B.A portfolio of two stocks both with variances of 10% where the correlation of the stocks is -0.5 Questions

4. Your portfolio holds 10% stock A, 10% stock B and 80% stock C. You got returns of $20 in stock A, $50 in stock B and $-10 in stock C last year. Calculate the weighted average of your returns. Questions

5. You have a portfolio of 2 stocks. Stock A has a variance of 15% and stock B 30%. The covariance of stock A and B is 5%. Calculate the variance of a portfolio containing 30% stock A and 70% stock B. Questions