4. CAPM Beta

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Из курса от партнера Indian School of Business

Trading Basics

359 оценки

Indian School of Business

Trading Basics

359 оценки

Курс 1 из 5 — Specialization Trading Strategies in Emerging Markets

The purpose of this course is to equip you with the knowledge required to comprehend the financial statements of a company and understand the various transactions that take place in the stock market so that you can replicate the strategies discovered by the extant academic literature. The first part of the course provides a brief introduction to financial statements and various common filings of firms. You will learn how to obtain information regarding a company's performance from them and use the information to build trading strategies. Next, you are taught basic asset pricing theories so that you will be able to calculate the expected returns of a stock or a portfolio. Finally, you will be introduced to the actual functioning of asset markets, type of players in the market, different types of orders and the efficient ways and opportune time to execute them, trading costs and ways of minimizing them, the concept of liquidity .etc. This knowledge is required to develop efficient algorithm to execute various trading strategies.

Из урока

Asset pricing theories

Before you start trading, you should first be able to calculate the expected return from a stock. The expected return comes from various asset pricing models such as Capital Asset Pricing Model (CAPM), Arbitrage Pricing Theory (APT) and Fama-French Three Factor Model. The purpose of this module is to equip you with the skills required to calculate the expected returns of a stock (or) a portfolio. After completing this module you will be able to calculate the expected returns of a stock.

1. Expected returns and risk6:27

2. Diversification5:58

4. CAPM Beta6:10

5. Multifactor Models5:55

7. Arbitrage6:32

8. Arbitrage-Free Price6:03

9. Risk Factors4:44

Познакомьтесь с преподавателями

Ramabhadran Thirumalai
Assistant Professor
Indian School of Business

Learning outcomes.

After watching this video, you will be able to

calculate the covariance between a risky asset's return and the market's returns.

Calculate the beta of a risky asset given expected returns,

standard deviations and covariances.

Calculating the CAPM beta.

Last time we saw the mathematical form of the CAPM and

the equation to calculate the CAPM beta.

Now we will apply this formula to calculate the betas of risky assets.

Let's go back to our three risky asset case, but

change the correlations a little.

Remember, we saw that the portfolio that has negative weights for

some risky assets cannot be a market portfolio.

In our previous risky asset example,

Z has a negative weight in the mean variance efficient portfolio.

To solve this problem, we'll change the covariances a little.

We continue to assume that there are only three risky and

one risk free asset in the entire world.

The expected return and standard deviation for X are 10% and 7% respectively.

Similarly for Y, we have 20% and 10% respectively and for

Z we have 15% and 12% respectively.

The covariance between X and Y is 0.0032,

that between X and Z, is 0.0013,

and that between Y and Z is 0.0054.

The risk free rate is still 5%.

Using solver in Excel, you can confirm that the weights of X,

Y, and Z in the mean radiance efficient portfolio are 0.0546,

0.8424, and 0.1030, respectively.

Since all the rates are positive,

this mean variance efficient portfolio is a valid market portfolio.

Remember how to calculate the expected return and

standard deviation of returns for a portfolio.

The expected return of the market portfolio is 0.0546 times 10%,

plus 0.8424 times 20% plus 0.1030

times 15% which gives us 18.94%.

The standard deviation of the market

portfolios returns is the square root of

0.0546 squared x 0.07 squared,

+0.8424 squared, x 0.10

squared, + 0.1030 squared,

x 0.12 squared, + 2 times 0.0546,

x 0.8424 x 0.0032 + 2 x

0.0546 x 0.1030 x 0.0013 +

2 x 0.8424 x 0.1030 x 0.0054.

The standard deviation of the market portfolio comes out to be 9.22%.

To calculate the betas of the three assets, we need to calculate

the covariance of each asset's returns with that of the market portfolio.

Remember, the market portfolio itself consists of 0.0546 in X,

0.8424 in Y, and 0.1030 in Z.

It can be shown that the covariance between Xs returns and

the market portfolios returns can be calculated as follows.

It is the covariance between X and

0.0546 of X plus the covariance between X and

0.8424 of Y plus the covariance of X and 0.1030 of Z.

The covariance between X and X is nothing but the variance of X.

So now we have 0.0546 times the variance of X

plus 0.8424 times the covariance between X and

Y plus 0.1030 time the covariance between X and Z.

This works out to be 0.0031.

You can similarly calculate the covariances of Ys returns and

Zs returns with the market portfolio's returns.

They work out to be 0.0092 and 0.0061, respectively.

I leave it up to you to do the calculations and verify these two numbers.

We can now calculate the betas of the three risky assets.

For X, it is the covariance of its returns with the market portfolio's returns, which

is 0.0031 divided by the variance of the market's returns, which is 0.0922 squared.

The beta comes out to be 0.36.

Similar calculations for Y and

Z yield betas of 1.08 and 0.72 respectively.

Please verify these numbers.

Do note that Y has the highest expected return of 20% among

the three risky asset and its beta of 1.08, is also the highest.

X, on the other hand has the lowest expected return of 10%, and

also the lowest paid of 0.36.

This is consistent with investors demanding a higher compensation in

the form of higher expected returns for holding riskier higher beta assets.

Next time we will define a plot of the gap M which is called the security market

client and compare it to the capital market client.

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