Capital Asset Pricing Model Hello everyone! This is Jamshidbek Jalilov, and I am pleased to welcome you in investment risks. Today we will have a lecture 8, which is capital asset pricing model or CAPM. Lecture 8

Introduction Modern Portfolio Theory and diversification Beta vs. standard deviation Unsystematic vs. systematic risk Security Market Line (SML) The CAPM equation Asset pricing Assumptions behind using CAPM We are going to cover the topics which you see on this slide.

Modern Portfolio Theory and diversification Rational investors use diversification to optimize their portfolios Diversification reduces portfolio risk (assets that are not perfectly correlated) Efficient Portfolio If you were to craft the perfect investment, you would probably want its attributes to include high returns coupled with low risk. The reality, of course, is that this kind of investment is next to impossible to find. Not surprisingly, people spend a lot of time developing methods and strategies that come close to the "perfect investment". But none is as popular, or as compelling, as modern portfolio theory MPT says that it is not enough to look at the expected risk and return of one particular stock. By investing in more than one stock, an investor can reap the benefits of diversification - chief among them, a reduction in the riskiness of the portfolio. MPT quantifies the benefits of diversification, also known as not putting all of your eggs in one basket.

Beta vs. standard deviation Standard deviation includes systematic and unsystematic risk; not used because unsystematic risk diversified away Beta: A standardized measure of the risk of an individual asset, one that captures only the systematic component of its volatility; measures how sensitive an individual security is to market movements; measure of market risk For most investors, the risk they take when they buy a stock is that the return will be lower than expected. In other words, it is the deviation from the average return. Each stock has its own standard deviation from the mean, which MPT calls "risk". Standard deviation as a statistical measure shows the distance from the mean of a sample of data, or the dispersion of returns from the sample’s mean. In terms of a portfolio of stock, standard deviation shows the volatility of stocks, bonds, and other financial instruments that are based on the returns spread over a period of time. As the standard deviation of an investment measures the volatility of returns, the higher the standard deviation, the higher volatility and risk involved in the investment. A volatile financial security or fund displays a higher standard deviation in comparison to stable financial securities or investment funds. A higher standard deviation is seen to be more risky as the investment’s performance may change drastically in any direction at any given moment. Beta measures a security’s or portfolio’s performance (asset’s risk and return) in relation to the movements in the market.  Beta is a relative measure used for comparison and does not show a security’s individual behavior. For example, in the case of stocks, beta can be measured by comparing the stock’s returns to the returns of a stock index such as S&P 500, FTSE 100. Such a comparison allows the investor to determine a stock’s performance in comparison to the entire market’s performance. A beta value of 1 show that the security is performing in line with the market’s performance and a beta of less than 1 show that security’s performance is less volatile than the market. A beta of more than 1 show that a security’s performance more volatile than the benchmark.

Systematic vs. unsystematic risk Systematic risk: risk that cannot be eliminated through diversification a.k.a, market risk or undiversifiable risk Unsystematic risk: risk that can be eliminated through diversification a.k.a. Unique risk, residual risk, specific risk, or diversifiable risk Modern portfolio theory states that the risk for individual stock returns has two components: Systematic Risk - These are market risks that cannot be diversified away. Interest rates, recessions and wars are examples of systematic risks. Unsystematic Risk - Also known as "specific risk", this risk is specific to individual stocks and can be diversified away as you increase the number of stocks in your portfolio (see Figure 1). It represents the component of a stock's return that is not correlated with general market moves.

Security Market Line Line representing the relationship between expected return and market risk; shows expected return of an overall market as a function of systematic risk Graphical representation of CAPM Compare a single asset to the SML (and see if it falls below, above, or on the line) The security market line (SML) is a line that graphs the systematic, or market, risk versus return of the whole market at a certain time and shows all risky marketable securities. Also referred to as the "characteristic line".

Security Market Line The security market line is a useful tool in determining whether an asset being considered for a portfolio offers a reasonable expected return for risk. Individual securities are plotted on the SML graph. If the security's risk versus expected return is plotted above the SML, it is undervalued because the investor can expect a greater return for the inherent risk. A security plotted below the SML is overvalued because the investor would be accepting less return for the amount of risk assumed.

Capital Asset Pricing Model (CAPM) The expected return on a specific asset equals the risk-free rate plus a premium that depends on the asset’s beta and the expected risk premium on the market portfolio. Expected return of specific asset: E(Ri) Risk-free rate: Rf Expected risk premium: E(Rm) - Rf

Practice Problem #1 If the risk-free rate equals 4% and a stock with a beta of 0.8 has an expected return of 10%, what is the expected return on the market portfolio?

Practice Problem #1: answer If the risk-free rate equals 4% and a stock with a beta of 0.75 has an expected return of 10%, what is the expected return on the market portfolio? 10% = 4% + 0.75(market portfolio – 4%) 6% = 0.75(market portfolio – 4%) 8% = market portfolio – 4% 12% = market portfolio

Practice Problem #2 A particular asset has a beta of 1.2 and an expected return of 10%. Given that the expected return on the market portfolio is 13% and the risk-free rate is 5%, the stock is: A. appropriately priced B. underpriced C. overpriced

Practice Problem #2: answer A particular asset has a beta of 1.2 and an expected return of 10%. Given that the expected return on the market portfolio is 13% and the risk-free rate is 5%, the stock is: A. appropriately priced B. underpriced C. overpriced; expected return should be 14.6% (5+1.2(13-5))

Asset pricing Future cash flows of the asset can be discounted using the expected return calculated from CAPM to establish the price of the asset If observed price > CAPM valuation  overvalued (paying too much for that amount of risk) If observed price < CAPM valuation  undervalued

Assumptions behind the CAPM U.S. treasuries are risk-free Uncertainty about inflation Assumed that investors can borrow money at same interest rate at which they lend, but generally borrowing rates are higher than lending rates WHY we still use CAPM: benchmark portfolios used  Treasury bills and market portfolio

Practice Problem #3 Last year… Firm A: return: 10%, beta: 0.8 Firm B: return: 11%, beta: 1.0 Firm C: return: 12%, beta: 1.2 Given that the risk-free rate was 3% and market return was 11%, which firm had the best performance?

Practice Problem #3: answer Firm A: 3% + 0.8(11%-3%) = 9.4% (over) Firm B: 3% + 1.0(8%) = 11% (same) Firm C: 3% + 1.2(8%) = 12.6% (under) Firm A performed the best because it exceeded the expected return