Lecture 6, Chapters 8.1-8.2, 9-10: Asset Pricing Models

1. What should a security yield with beta 1? 2. What should a security yield with beta larger than 1? 3. What should a security yield with beta of 2?

1. Beta 1 = The market excess return 2. Beta larger than 1 = more than the market excess return 3. Beta 2 = should yield twice the market excess return

The total risk of a specific stock's returns consists of:

1. Risk that can be related to the market (aka systematic risk) 2. Idiosyncratic risk i.e. firm specific risk (aka unsystematic risk)

What is Alpha?

Alpha is abnormal return. Is the rate of return beyond the value that would be forecasted from the market's return and the systematic risk of the security. A basic calculation of alpha subtracts the total return of an investment from a comparable benchmark in its asset category. True 𝛼's are hard to find and cannot persist for long, so passive investing is an appealing approach.

Are securities above the SML (market security line) over or underevaluated?

Anything above the SML (securities market line), is undervalued. Is too cheap.

What is arbitrage?

Arbitrage is basically buying a security in one market, and simultaneously selling it in another market at a higher price, profiting from the temporary difference in prices. This is considered risk-free profit for the investor/trader.

What is the Arbitrage Pricing Theory (APT)?

Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea that an asset's returns can be predicted using the linear relationship between the asset's expected return and a number of macroeconomic variables that capture systematic risk. If you can identify the correct factors that affect expected return, then you can replicate the asset by investing in those factors in the right proportions. If the price of the asset deviates from the factor portfolio, there will be an arbitrage opportunity - If the asset is more expensive than the factor portfolio, then investors will sell the asset and buy the factor portfolio - The asset will decrease in value in relation to the factor portfolio - The investor will make a profit (in theory a risk free profit, arbitrage)

What Is Beta and how does the formula looks like?

Beta is the systematic or market risk of a security. Beta is a measure of the volatility of an investment compared with the market as a whole. The market has a beta of 1, while investments that are more volatile than the market have a beta greater than 1 and those that are less volatile have a beta of less than 1. The Formula for Beta Is ​ Beta coefficient(β) = Covariance(Re,Rm) / Variance(Rm) where: Re = the return on an individual stock Rm = the return on the overall market Covariance = how changes in a stock's returns are related to changes in the market's returns Variance = how far the market's data points spread out from their average value ​

What assets is the Market Portfolio composed by?

Equities and bonds. When combined, we look for the optimal risky portfolio.

What are the assumptions of CAPM?

For the individual investor's behaviour: - Investors are rational, and they don't change depending on how the market goes. - Investors are mean-variance optimazers, mening that they care only for return and risk. - Their planning horizon is a single period -Investors have homogeneous expectations, mening they have identical input lists = they all would answer the same expected return for a stock. For the market structure: - All assets are publicly held and trade on public exchanges, short positions are allowed and investors can borrow or lend at a common risk-free rate. - No taxes. - No transaction costs.

If a stock have a positive alpha (rate of return), will the price and the yield go up or down?

If a stock have a positive alpha, the price will go up, and the yield go down. The potential upside will be eating by the increased price.

If the CAPM holds, what should the alpha (rate of return) be?

If the CAPM holds, alpha should be zero.

Name differences between Markowitz model and the single index model

In the Markowitz method there are few assumptions, but many estimates. In the Single Index method there are many assumptions but few estimates.

Describe the Markowitz model

Markowitz model: a clean model with few assumptions where all assets are correlated with each other when calculating risk and return for the portfolio. Many estimates need to be calculated which makes it an impractical model and not all results make sense. This is a theory on how risk-averse investors can construct portfolios to optimize or maximize expected return based on a given level of market risk, emphasizing that risk is an essential part of higher reward.

What are the advantages and disadvantages of the Markowitz model, the single factor model and the multi factor model?

Markowitz model: a clean model with few assumptions where all assets are correlated with each other when calculating risk and return for the portfolio. Many estimates need to be calculated which makes it an impractical model and not all results make sense. Single Index model: Instead of correlating all assets with one another, all assets are correlated with the market resulting in a risk factor called Beta. This is a more practical approach but more assumptions, for instance; is one risk factor enough? Multi-factor model: Like the single-Index model but with more risk-factors to capture risk but it is unclear how many factors are enough. Many assumptions and estimates when trying to establish the right amount of risk-factors

Describe the multi-factor model

Multi-factor model: Like the single-Index model but with more risk-factors to capture risk but it is unclear how many factors are enough. Many assumptions and estimates when trying to establish the right amount of risk-factors

What is the difference between CAPM and APT?

The CAPM assumes that market returns represent systematic risk. The APT recognizes that other macroeconomic factors may be systematic risk factors.

If I want to find an asset that gives me high returns, what does CAPM tells me?

The CAPM tells you: chose asset with high systematic risk (Beta)!

What is CAPM?

The Capital Asset Pricing Model. It defines the relationship between risk and return. A stock's expected performance is based on its beta (risk) compared to that of the stock market. More risk : more expected return.

Describe the single index model

The single-index model (SIM) developed by Sharpe, is a simple asset pricing model to measure both the risk and the return of a stock. Instead of correlating all assets with one another, all assets are correlated with the market resulting in a risk factor called Beta. This is a more practical approach but more assumptions, for instance; is one risk factor enough? CAPM and SIM are directly linked to each other. The index model is based on the following: Most stocks have a positive covariance because they all respond similarly to macroeconomic factors. However, some firms are more sensitive to these factors than others, and this firm-specific variance is typically denoted by its beta (β), which measures its variance compared to the market for one or more economic factors. Covariances among securities result from differing responses to macroeconomic factors. Hence, the covariance of each stock can be found by multiplying their betas and the market variance.

What is the difference between the SML (security market line) and the CML (capital market line)?

They use different measure of risk! CML uses standard deviation. SML uses Beta. CML shows the rates of return for a specific portfolio and uses standard deviation as measure of risk. SML represents the market's risk and return at a given time, and shows the expected returns of individual assets, and the risk measure in the SML is systematic risk, or beta.

What is the Security Market line?

This is line showing the relationship between risk and return. The y-axis is expected return, the x-axis is risk in form om the Beta. The line is straight and slopes upward and to the right meaning that investors require a greater expected return as risk increases.

What happens with the firm specific risk in the single index model?

When several assets are combined, the firm specific risk (aka unsystematic risk) gets diversified away and you are left with the portfolios relation to the market risk. By increasing the number of assets in the portfolio (diversification), the unsystematic, i.e. the risk due to firm-specific factors, can be reduced to zero.