The Capital Asset Pricing Model (CAPM) by William Sharpe. | by Dimitrios Gourtzilidis | Jul 2022

Continuing modern portfolio theory and quantitative finance, the next step is the analysis of the Capital Asset Pricing Model (CAPM).

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William Forsyth Sharpe, born in 1934, is an American economist and one of the creators of the Capital Asset Pricing Model (CAPM), along with John Lintner (1916-1983) and Jan Mossin (1936-1987). He holds an undergraduate degree from the University of California in Business Administration with a major in Economics.

It was during this period that he was introduced to Harry Markowitz “Portfolio Selection” paper, which we analyzed in the article “Harry Markowitz: the father of modern portfolio theory”. They even worked together in the same company, the RAND Corporation.

Ten years after the publication of Professor Markowitz’s article, William Sharpe expanded on this subject by attempting to publish his own article in the Journal of Finance in 1962. His article stood under review and was rejected until ‘ in 1964, when it was finally published under the title “Fixed Asset Pricing — A Theory of Market Equilibrium Under Conditions of Risk”. This work earned him the Nobel Prize in Economics in 1990.

William Sharpe was a professor of finance at Stanford University until 1989, when he retired from teaching and started his own consulting firm “William F. Sharpe Associates”. In 1996, he launched “Financial driversnow known as “Edelman Financial Engines”, a company that provides wealth management services to individuals.

“The investment decision was really quite simple. If you had access to a real, really diversified broad market portfolio, you just split your money between that and something low or very low risk…we could characterize your preferences as some measure of risk aversion versus the money you have the day you retire.”

—William F. Sharpe

The CAPM model is the relationship between the price of an asset, its risk and its expected return and the basic principle is the maximization of the returns of a portfolio according to the risk tolerance and the profile of its holder. As the name suggests is a “asset valuation modellike many others.

As we have seen, Professor Markopwitz also worked in this way, but William Sharpe simplified the process. With the fixed asset valuation model, we can calculate whether a stock is “undervalued” or “overvalued” based on its risk and expected return.

The formula begins by taking into account the returns of a risk-free asset (Rf). The reason is that we, the homo economicus, will not invest in something that produces less return on the risk-free asset, but increases our risk. The yield on the risk-free asset, i.e. the 10-year US Treasury, is currently yielding 1.9%, as we can see below on the MarketWatch.com webpage .

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We’ll look at the beta later. Right now we’re going to look at subtraction inside the parenthesis. This is called the “market risk premium”. The performance of a single stock, Professor Sharpe said, depends on the performance of the whole market after subtracting the risk-free rate. Let’s say the market produces a return of 10% and the risk-free asset a return of 5%. With this in mind, our market premium will be 10% to 5% = 5% of the additional return, if we are willing to accept the additional market risk relative to the risk-free asset.

The return of the whole market is usually around 7% according to investopedia.com.

Beta

Simply put, beta is a variable that can take on values ​​between 0 and 2 in general terms, and it measures a stock’s reaction to a particular market movement.

1 means it follows the market exactly. A 5% move in the market will trigger a 5% move in the asset. If the asset has a beta value of 2, that means a 5% market move will trigger a 10% asset move. A negative beta, on the other hand, indicates that the asset is moving counter-cyclically relative to the market.

Another interpretation would be that any asset with less than 1 beta is less risky than the market as a whole. On the other hand, any asset above 1 is riskier than the market. An asset with a beta value of 1.20 has 20% more systematic risk than the market.

Many websites, of course, have calculated the beta of each asset, so we don’t need to calculate it from scratch.

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The beta formula of an asset is as follows.

Under Beta, the CAPM model, we understand that the only risk investors are compensated for is systematic risk. This expands on Harry Markowitz’s MPT.

As we have seen, the CAPM formula applies to portfolios as well as individual stocks. The only note to consider with individual stocks is that the formula does not take into account the percentage of risk that could be diversified when that single stock was combined with other assets.

Every investment involves risk, but not all risks are equal. If we were to have an asset, we would assume the risk it carries. If we combined this asset with another and formed a portfolio, we could diversify some of the risk carried by both. That’s what we call “unsystematic or idiosyncratic risk”.

The part of the risk that no matter what we do we can’t run away or diversify is called “systematic risk”, “market risk” or beta. This is the only risk worth paying for in our wallet.

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For example, the risk an investor had in their portfolio during the Great Depression era could not be diversified. This black swan event beyond our control hit the global economy and therefore could not be diversified.

Unlike MPT, CAPM calculates risk based on beta, not total risk.

The Security Market Line (SML) is a similar concept to the Markowitz Capital Market Line (CML).

A key difference is that CML uses total risk, and SML measures based on systematic risk. This difference separates the CML model which can only be applied to already fully diversified portfolios, while the SML is more flexible and can be used for any individual asset or portfolio.

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“I don’t bet on the success or failure of a business. I simply view companies as investment opportunities that offer certain expected returns, volatilities, and covariances. You want to go the Warren Buffett way, and I resist that because I don’t have the skills of a Warren Buffett. So I don’t know what’s good and what’s not… Do you really believe that Campbell’s Soup or Wal-Mart should be the companies you invest in today? I don’t know…unless you’re prepared to make predictions, it’s the only alternative that offers a disciplined approach to investing in so-called good portfolios.

— Andrew Lo, professor of finance at MIT

William Sharpe created the Sharpe ratio to compare different portfolios based on their risk and return. This equation does not compare an asset or a portfolio according to a benchmark like the market risk premium. It’s just a measurement of risk-adjusted returns.

“I took in-house courses on programming and loved it. I also loved algorithms…so I got hooked on programming, even creating a programming language and a compiler. I still program almost every days.

—William F. Sharpe

Of course, no model is perfect. Each model and theory has its own limitations. CAPM takes into account, for example, a world in which:

  • We have no transaction fees and no taxes.
  • Assets are infinitely divisible and liquid.
  • Investors follow the rational model of homo economicus.
  • And finally, a world in which everyone has effective wallets.

CAPM is a model that has proven to be correct in most cases and has been used for many decades in the financial industry.

For the novice investor, the thing that may need to be taken into account is that William Sharpe was always a strong advocate of a broadly diversified portfolio, and this idea later gave rise to the index fund market.

Robert D. Coleman