When someone hears I am currently writing a licensed biographer of William (Bill) Sharp, the most frequent question I get is, “Is he still alive?” Sharp was awarded the Sveriges Rikbank Award in Economic Sciences in commemoration of Alfred Nobel, known as the Nobel Prize in Economics in 1990. And yes, in September 2024, he is still alive and well. He lives in every Carmel in California. Every Thursday morning he meets with the coffee clutch. He can often be seen walking the Vicon Poodle near Carmel Bay. In June 2024, he celebrated 90th birthday.
September 2024 was another sharp milestone. Financial Journal. Not to mention six, it is very rare for a study to remain relevant even after 10 years. I will explain what the paper is, how it impacted the investment industry that is most likely to include your own portfolio, and why it is still important.
Photo by Stephen R. Foerster
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Let's talk about the model's name, the common acronyms, and what it really is. First, Sharp never called it a “capital asset pricing model.” As the title of his original article suggests, it is about “capital asset prices.” Later, researchers called it a model, and M. Once the second was added and it became known as the capital asset pricing model, it was introduced by the acronym Capm, pronounced “Cap-Em.”
Virtually every finance professor and student calls it “Cap-Em.” Everyone except Sharp himself. He always uses initialization CAPM. (So if you want to honor the creator of the model, you can call it CAPM!) One of the key insights in CAPM is to answer key investment questions. “What revenue would you expect from purchasing Security XYZ?”
Important assumptions
Sharpe wrote a paper in 1963, “Simplified Models for Portfolio Analysis,” and presented some of the same important concepts as the original 1964 paper. There is an important difference between the two papers. As Sharp later explained, in a 1963 paper, he “put a rabbit in a hat” before pulling it out. The 1963 paper also answered the important question, “What is the expected revenue of purchasing a security xyz?”
However, the rabbit he put in his hat was a pre-determined relationship between security and the entire market. Andrew Law and I interviewed Sharp for our book, Pursuing the perfect portfolio: The stories, voices, and important insights of the pioneers who shaped the way we invest. “So I spent several months trying to find a way to do it without putting rabbits in their hats,” he said. “Was there a way to pull a rabbit out of the hat without first putting on a hat? Yes, I thought there was.” In a 1964 article, Sharp didn't put the rabbit in the hat, but rather theories. We derived market equilibrium based on this.
Any theory needs to make assumptions to simplify what happens in the real world so that the theoretical model can provide traction. That's what Sharp did. He assumed that everything investors care about is the expected return and risk. He assumed that investors were reasonable and sufficiently diverse. He then assumed that investors could borrow and lend the same rate.
When Sharp first submitted his paper for publication Financial Journal, It was rejected primarily due to Sharp's assumption. The anonymous judge concluded that Sharp's assumptions were so “idiotious” that all subsequent conclusions were “not interesting.” Two years later, Sharpe made some paper adjustments, found a new editor, and the paper was published. As they say, the rest is history.
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Many of Sharpe's classic papers focus on nine figures or graphs. The first seven are in two-dimensional space, with risk measured by standard deviations on the vertical axis and expected rate of return on the horizontal axis. (Finance students immediately note that current practice is to flip the axis, which represents the risk of the horizontal axis and the expected return of the vertical axis.)
On his horizontal axis, Sharp began with a special security return that he called “pure interest rates” or P. Today we call that special fee a return of the Treasury bill, or a commonly expressed risk-free interest rate. As RF.
Curve Igg' is Harry Markowitz's efficient frontier. This allows for the “optimal” combination of risky securities and the risk of the expected return at a certain level, so that each portfolio on the curve has the highest expected return at a certain level. It's going to be lower. Sharpe's model essentially sought a risk-free combination of security Ps. Each portfolio is on the curve IgG', which provides the expected returns with optimal risk. From the graph, it is clear that the optimal mix is formed by the line from P that tangent to the curve with IgG'. In other words, it is a mix of risk-free assets P and portfolio G.
In the Sharp world, investors can be thought of as having three options essentially. She can invest all her money in a dangerous portfolio g. If that's too much risk for her, she can divide her portfolio into a combination of riskless P and risky G. Or, if she wants more risks, she can borrow at a riskless rate and invest more than 100% of her wealth in a risky G, essentially on the line towards Z. You can move along. The best combination of riskless and risky investments, including either lending (purchasing Treasury invoices) or borrowing (Treasury bill rate).
Nobel Prize-winning footnote
After presenting a series of graphs, Sharpe showed that this could lead to a relatively simple formula that “also relates the expected rate of return to various risk factors for all assets contained in combination G.” He then introduces the reader to footnote 22. This is an extensive 17-line equation and text that could be one of the most consequential footnotes in all financial and economic literature.
The last line of the footnote may not look familiar, but we'll focus a bit by hand. Sharp gave the new name on the left: Big, “IG” is a subscript. Technically speaking, the covariance of security return I for security G is divided by the standard deviation of g. When creating the manuscript, Sharpe used a typewriter with standard keys. What he really meant by B was the Greek letter B or beta. And, as we see, it has become one of the most used risk measures today.
Something that promotes expected returns?
One important insight from Sharpe's model is that everything that matters is either big or beta when it comes to expected returns for security.
In Sharpe's final graph, the expected return is still on the horizontal axis, but his new measure of risk, Big or Beta, is on the vertical axis. Now the line PQ actually becomes the CAPM equation. What it shows strongly is that, assuming investors have a well-diversified portfolio, the only measure of significant risk is beta, or how dangerous is the security of the entire portfolio? It's about whether it is. All investors want to hold G, so they should include all their assets. In other words, it must be a market portfolio. Today we call that portfolio M.
You can rewrite the original derivative of Sharpe into a more familiar version: E(ri)=rf + bx [E(Rm) – Rf] Or e(ri)=rf + bi x mrp. Here we represent Security I, and MRP is the market risk premium. This is intuition. Let's assume you are considering investing in stocks for the next 10 years. Alternatively, you could invest in the Long-Term Treasury Department to ensure RF returns. Alternatively, you can invest in the entire market and earn your expected returns of E(RM). This turns out to be the same as RF + MRP. Or, finally, you can invest in security. Your expected return, E(RI) is driven by how much market risk you are exposed to, bi.
Beta has a simple interpretation of how dangerous a particular security is compared to the overall market. As for benchmarks, by definition the beta version of “market” is 1.0. For certain security, beta suggests what a change in a specific return is for every 1.0% change in the market. For example, if the market (often relying on the S&P 500 index) rises by 1.0%, then inventory is expected to rise by 0.5%. If the market is down 1.0%, we expect inventory I to fall by 0.5%. For example, the same logic applies to beta 1.5 risky inventory. If the market rises 1.0%, inventory I is expected to rise 1.5%. If the market is down 1.0%, we expect inventory I to fall 1.5%.
Why is CAPM important?
Sharpe's inventive 1964 paper is important for three reasons:
- Beta is a good measure of the risk of equities, which are part of a diversified portfolio. Also, Yahoo! It is also a measure widely available on sites such as Finance. What's important is risk compared to the market. If you have a diversified portfolio, it doesn't matter how volatile your inventory is.
- Sharpe's model shows Figure 7 in a sense, showing how to measure performance across a well-diversified portfolio, such as mutual funds. Over the past five years, we can measure the performance or return of a fund beyond what risk-free investments are returned. That's the return scale. Comparing it to the fund's risk, there is a risk-to-return measure, as measured by a standard deviation in the fund's return over that period. This was explained by Sharp in his subsequent research papers and became known as the Sharp ratio. It is probably the most common measure of performance today.
- In Sharpe's CAPM paper, he defined his special portfolio G. G is something that everyone wants to hold as representing “all assets.” So we call it a market portfolio. A narrower interpretation requires at least all inventory to be included. Inherent to the US, this means purchasing index funds that replicate the S&P 500 index. Sharpe's model is grateful for the trillion dollar index funds that have appeared over the past 50 years. You may be invested directly or indirectly in an index fund through a pension fund.
Of course, CAPM has critics. There are several competing models of expected returns that will acquire additional factors beyond the market. There are some suspicious empirical test results. Still, this model remains the front and center of a financial course and is used by practitioners. And it's a very intuitive model. It has stood the test of time.
So happy birthday to Cap.
