ML4T笔记 | 02-04 The Capital Asset

2019-02-19 本文已影响8人我的名字叫清阳

01 - The Capital Asset Pricing Model

CAMP is one of the most significant ideas affecting finance in the last century.
CAMP explains how the market impacts individual stock prices.
CAMP provides a mathematical framework for hedge fund investing.
It was developed by a number of researchers independently in the 1960s.
William Sharpe, Harry Markowitz, and Merton Miller jointly received the Nobel Prize for this contribution in 1990.
The CAPM led to the development of index funds and the belief that you can't beat the market

Time: 00:00:36

02 - Definition of a portfolio

Definition: A portfolio is a weighted set of assets.

E.g.: a portfolio that's got three different assets in it, Apple, Google, and Oracle. 60% in Apple, 20% in Google, and 20% in Oracle.
- 60%, 20% are the weights (w_i)
- $\sum abs(w_i) = 100\%$ ( leveraged portfolio is a exception).
- returns on a portfolio: $R_p(t) = \sum_{i =1}^{n}(w_i * R_i(t))$ , n = number of stocks in the portfolio.
- the equation allows short porsition and the return of it is opposite to the markect change.

ime: 00:02:05

03 - quiz Portfolio return

weight	stock	return	Position
75%	A	1%	Long
-25%	B	-2%	Short

Given the portfolio and return of the stocks in it, calculate portfolio return

Solution:
portfolio return = 75% * 1% + (-25%) * (-2%) = 1.25%

the weight for Stock A is .75 and the return is 1%
the weight for Stock B is negative 25% and return is 2% .
since we shorted B and it went down, we got a positive component there, or .5.

Time: 00:00:39

04 - The market portfolio

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The Market Portfolio usually referring to is an index that broadly covers a large set of stocks.

e.g. S&P500. The S&P 500 represents the 500 largest companies that are traded
The index changes each day according to the prices of all of its components.

The market portfolio is a combination of those stocks in a certain weighting.

Cap Weighted: the weight of each stock in the index portfolio is usually set according to that stock's market cap ( $w_i = number\ of\ shares_i * price_i / \sum_{j=1}^{n}(market\_Cap_j)$ ).

Sectors

the US we typically break the market into ten different sectors, list four of them here. E.g.: Energy, technology, manufacturing, finance and so on.
positive and negative news can affect each of these sectors individually without necessarily affecting the others.

So it's not unusual to break up these large markets into individual sectors.

Note: some stocks have surprisingly large weightings (e.g. Apple and Exxon each are about 5% of the S&P 500) thus have a strong effect on what happens to this index.

Time: 00:03:46

05 - The CAPM equation

The capital assets pricing model equation.

$r_i(t) = \beta_i * r_m(t) + \alpha_i(t)$

$r_i(t)$ : The return of a particular stock, i, on a particular day,
$\beta * r_m(t)$ : the return for a particular stock due to the market.

the market moving up or down strongly affects the change in price on every individual stock and $\beta$ is the extent of effects.
every stock has it's own $\beta$ .
$alpha$ is called the residual which is the part that $beta$ cannot predict.
In the capital assets pricing model, the expectation for $alpha$ is 0.

Where do we get this beta and this alpha?

Depends on how the daily returns for a particular stock $r_i(t)$ relate to the daily returns of the market $r_m(t)$ .

plot returns here for S&P 500 ( $r_m(t)$ .) against the daily return of an individual stock xyz ( $r_i(t)$ .) and fit a line to it. Then $beta$ is the slop and $alpha$ is the y-intercept.
$alpha$ and $beta$ is based on historical data. in CAPM $alpha$ are expect to be 0 (not always 0 in reality)

Time: 00:04:21

06 - quiz: Compare alpha and beta

Of the two plots, which one has higher alpha and which one has a higher beta?

Solution:
Correlated with SP500, ABC clearly has a greater slope than XYZ, therefore higher β. It also has a larger Y-intercept (α).

Time: 00:00:36

07 - CAPM vs active management

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passive investing: essentially says that you should just buy an index portfolio, hold and let it grow.
Active investing: Active portfolio managers don't just buy the index portfolio, they pick individual stocks. s/he weights some stocks higher and others lowers, and select higher weighted ones for his/her portfolio

consider passive versus active in that context

Both active managers and passive managers agree that the stock moves each day is most significantly influenced by the market $beta * r_m(t)$ .
The CAPM the $\alpha$ is 1) random and 2) expected to be zero.
Active managers believe they can predict alpha relative to the market.
a passive investor believes the capital assets pricing model,
Just buy an index and hold it.
and active investor believes they or some else can find alpha.

Time: 00:03:07

08 - CAPM for portfolios

the return for the entire portfolio

compute this return for each individual stock $r_i(t)$ , multiply it by the weight for that stock and then we take the sum across all the stocks.
$r_p(t) = \sum(r_i(t) * w_i)$ (remember $r_i(t) = \beta_i * r_m(t) + \alpha_i(t)$ )

New way to calculate Beta

$\beta_p = \sum(w_i(t) * \beta_i)$ and $\alpha_p = \sum(\w_i(t) * alpha_i(t)$
Thus,
$r_p(t) = \beta_p * r_m(t) + \alpha_p$ for CAMP
$r_p(t) = \beta_p * r_m(t) + \sum_i(w_i * alpha_i(t)$

Time: 00:02:04

9 - quiz: Implications of CAPM Quiz

Consider the implications of the CAPM, and implications in upward markets and downward markets.

If we're in upward markets, do you want a larger beta or a smaller beta? And if we're in downward markets, do you want a larger beta or a smaller beta?

solution:

market	stock
Upward	larger
Downward	smaller

Time: 00:00:28

10 - Implications of CAPM

alpha is random, and the expected value of alpha is zero.
the only way we can beat the market now is by cleverly choosing $\beta$ , high beta and up markets and low beta and down markets.
the efficient markets hypothesis says you can't predict the market which means $\beta$ is not predictable.
taken together, CAMP and the efficient markets hypothesis say that you can't beat the market.

Now, we are on to ways that you can potentially beat the market

Time: 00:01:31

11 - Arbitrage Pricing Theory

Arbitrage Pricing Theory was developed by Stephen Ross and first published in 1976.
Dr. Ross though using single beta that represents a particular stock's relationship to the market is not enough; Maybe multiple $\beta s$ against different sectors.
And of course we still have our $\alpha$ .
$r_p(t) = \beta_{iF}*r_F + \beta_{iT} * r_T + \beta_{iM} * r_M + ... ... + \alpha_i$

Time: 00:01:38

Total Time: 00:22:12

2019-02-18 初稿