Returns are usually expressed as a performance number- either as a $ return or as a percentage. Therefore we need to be able to measure the level of risk inherent in a potential investment, and we also need to be able to calculate the expected return for that risk. Risk is not achieving the return that is expected We measure risk by calculating variance and standard deviation – these show the volatility of the returns – the higher the volatility the higher the uncertainty, the higher the risk.
Look at the chart on IPPP – showing the probability distribution of two companies’ expected rates of return. Probability shows the chance that the event will occur, so the chart shows the possible returns that could occur from holding the two stocks. One has a very wide distribution of probabilities – therefore more volatile results so higher risk. The other stock has a much narrower range of possible returns therefore is lower risk. Standard deviation Historical variance is the sum of the squared deviations from a mean divided by the number of observations minus one.
Diversification The above call works because the two stocks perform differently In the two economic negative correlation – see example on IPPP. A portfolio made up from a group of tock all invested in the Alberta oilcan’s is not a diversified portfolio because they will have positive correlation. Stand-alone risk is the risk taken by holding Just one stock. Portfolios reduce risk by removing stand alone risk. An efficient portfolio is one where you hope to achieve the highest expected return for a given level of risk.
Or the lowest degree of risk for a given rate of return. By increasing the number of assets held in a portfolio the investor can reduce risk by removing the stand alone or company specific risk. But this only works up too number of assets held – see IPPP for chart showing non diversified risk. E an investor can diversify to remove stand alone risk but you cannot remove the non diversified risk. Stand alone risk = Unsystematic risk – ‘e unique to the company – related to its profits, competitive strengths etc.
Systematic risk = this undesirable risk. Economic factors affect this, egg consumer demand, GAP growth, currency, interest rates…. … Since the unsystematic risk can be diversified away by creating a portfolio of stocks, we have to be able to measure the systematic risk which can’t be diversified away. Beta Co- efficient Used to measure systematic risk. It shows how much systematic risk a stock bears marred to the average stock. Market average risk has a beta of 1 – a stock with less than average systematic risk has a beta of less than 1 – a stock with more than the market average systematic risk has a beta of higher than 1 – there is the risk free rate of return as represented by a short term Government bond or treasury bill – this has a beta of O ii no systematic risk We can calculate a portfolio beta in Just the same way as we call a portfolios expected return. Egg a portfolio invested 50% in A and 50% in B A has a beta of 0. 56 and B has a beta of 3. 28 The portfolio beta . 5 (3. 28) = 1. 92 Look a chart on IPPP
Read IPPP key points related to beta. The Security Market Line See chart on IPPP As the level of beta on the horizontal axis increases the expected return on the vertical axis increases = ‘e the line is upward sloping. We expect the line to be upward sloping because it is showing the reward for bearing (systematic) risk so more risk requires more reward. The slope of the line is equal to the Market Risk Premium ii the reward for bearing an average level of systematic risk. The equation describing this SMS is: RE = RFC +b(ERm – RFC) Where RFC is the risk free rate, ERm is the expected return on the market. This is the
Capital Asset Pricing Model To recap: Total risk – measured by standard deviation Total risk = unsystematic risk plus systematic risk Unsystematic risk can be diversified away by diversification Systematic risk can’t be diversified away. The higher the beta the higher the systematic risk in the asset. The higher the beta, the higher the expected return required to compensate for the systematic risk. Egg 2 stocks C and k SD seta c 2. 25 K 0. 5 Which stock has the higher total risk – Chick stock has the higher systematic risk – Chic stock should have the higher expected return – Suggested problems all questions problems –
