[Finance] The Capital Assets Pricing Model (CAPM)

CAPM provides a mathematical framework for hedge fund investing
  • It explains how the market impacts individual stock prices


    CAPM
  • r is return

  • i is a particular stock

  • r_i(t) is return of a particular stock on a particular day

  • m is market

  • r_m(t) is return on the market for that day

  • The capital assets pricing model says that significant portion of the return for an individual stock on a particular day is highly dependent on the market

  • \beta_i is the extent to which the market affects a particular stock, and it’s also the market

  • \alpha_i is the residual - so if you look at all the stocks over one day and look at how much the market goes up or down and you calculate how much the stock should have gone up or down according to \beta, there’ll be something left over. It won’t exactly match what \beta predicted and that’s what this alpha or residual component is

  • CAPM says that the expectation for \alpha_iis always 0: E = 0

  • \beta_iand \alpha_icome from daily returns and essentially how the daily returns for a particular stock relate to the daily returns of the market.

  • slope(\beta_i) and intercept(\alpha_i)

    beta and alpha

  • The general idea here is that the active portfolio manager’s portfolio differs from the market portfolio by selecting different weights on different stocks

  • Both active and passive managers agree with \beta_i r_m(t) as in how the stock moves each day is most significantly influenced by the market and that the amount that it moves is strongly related to \beta

  • Where they differ is \alpha_i(t) is with regard to their treatment of \alpha

Passive Managers
  • \alpha is random, you can’t predict it
  • The expected value is zero, E(\alpha) = 0
  • Some days it will be positive, some day it will be negative
  • It may be large, it may be small, but it’s random and on average the value will be zero
Active Managers
  • Believe they can predict \alpha
  • They can compare two stocks and they say: “I think this one is going to go up or down relative to the market”
  • They may not be exactly right on every single pick but they believe on average they’re better than just flipping a coin
  • If you believe active managers, you can use information and machine learning to find stocks that have either positive or negative \alpha and you can use that information to select your stock picks
If you believe the CAPM then you should be a passive investor - just buy an index and hold it
If you believe active managers that they can find \alpha then you should consider being an active investor
CAMP for portfolio
  • Active Manager will say yes, I agree that the \beta component is the same as CAPM says, but I think I can find value in this \alpha and it needs to be broken out individually
    active manager
In Upward Markets

You want a higher \beta in upward markets so that you can ride the surge

In Downward Markets

But a lower \beta in downward markets so you don't crash as much

CAPM says you can’t beat the market
If CAPM is true, we can’t beat the market
We don’t believe that and this whole course is about ways that you can potentially beat the market - so we’re getting to these eventually but CAPM is a reference framework for all the other things
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