<p>In the words of <a href="http://www-personal.umich.edu/%7Ekathrynd/JEP.FamaandFrench.pdf" rel="nofollow noreferrer">Fama &amp; French, The Capital Asset Pricing Model:
Theory and Evidence, Journal of Economic Perspectives—Volume 18, Number 3—Summer 2004—Pages 25–46</a>,</p>
<blockquote>
<p>The problems [of CAPM] are serious enough to invalidate most
applications of the CAPM.</p>
<p>The CAPM, like Markowitz’s (1952, 1959) portfolio model on which it is
built, is nevertheless a theoretical tour de force. We continue to
teach the CAPM as an introduction to the fundamental concepts of
portfolio theory and asset pricing, to be built on by more complicated
models like Merton’s (1973) ICAPM. But we also warn students that
despite its seductive simplicity, the CAPM’s empirical problems
probably invalidate its use in applications.</p>
</blockquote>
<p><a href="https://en.wikipedia.org/wiki/Capital_asset_pricing_model#Problems" rel="nofollow noreferrer">Wikipedia</a> offers a good collection of problems of the CAPM model. I honestly think that the risk free rate assumption is one of the smallest problems of the whole idea.</p>
<p>It is the second highest entry in the list of the most dangerous concepts in quantitative finance work on <a href="https://quant.stackexchange.com/a/157/54838">Quantitative Finance SE</a>, with correlation being the first one in the list. Since you compute beta using correlation...</p>
<p>That said, individual investors are not the major players and institutional investors can for example use REPOs with government bonds as collateral that trade in line with risk free rates. There are several similiar funding vehicles available.</p>

CC BY-SA 4.0
2022-10-13T13:32:15.160Z
Thanks! Hillier et al. "Fundamentals of Corporate Finance: 4th European Edition" (2022) states in chapter 13 that CAPM is still very widely by companies for estimating cost of capital and is actually the most popular method for that purpose. So I guess it must be worth something. My question can be seen in that context.
Richard Hardy
CC BY-SA 4.0
2022-10-13T21:26:57.453Z
One of the most widely cited problems with WACC is the use of beta. The benefit of CAPM is its simplicity and speed of computation. Also, what is an alternative? The Dividend Discount Model? Valuing companies based on spreadsheets of cashflows of some sorts or past prices is usually limited by design. In my experience, corporate finance, accounting/controlling is often very mechanical and follows simple rules. At least partly also because teams notoriously lack personnel, but also that results need to be communicated and explained to superiors. It's a safe bet to do what everyone else does.
AKdemy
CC BY-SA 4.0
2022-10-12T20:51:59.240Z
2022-12-15T00:06:28.080Z
2022-12-15T00:06:28.080Z
AKdemy
<p>In a presentation of CAPM, I have found an assumption that actors can borrow risk-free. If the borrowed money is to be used for investing in shares (which is a risky investment), it makes little sense to me that any lender would be willing to lend money at a risk-free rate. <a href="https://www.investopedia.com/articles/investing/021015/advantages-and-disadvantages-capm-model.asp" rel="nofollow noreferrer">Investopedia</a> mentions the same assumption and criticizes it as well:</p>
<blockquote>
<p><strong>Ability to Borrow at a Risk-Free Rate</strong><br />
CAPM is built on four major assumptions, including one that reflects an unrealistic real-world picture. This assumption—that investors can borrow and lend at a risk-free rate—is unattainable in reality. Individual investors are unable to borrow (or lend) at the same rate as the U.S. government. Therefore, the minimum required return line might actually be less steep (provide a lower return) than the model calculates.</p>
</blockquote>
<p>How big of a problem is that empirically? If it is not big, what mitigates it?</p>

<asset-pricing>
Risk-free borrowing as an assumption for CAPM
Richard Hardy
# Risk-free borrowing as an assumption for CAPM

(Asked by: username_0 on 2022-10-12)

In a presentation of CAPM, I have found an assumption that actors can borrow risk-free. If the borrowed money is to be used for investing in shares (which is a risky investment), it makes little sense to me that any lender would be willing to lend money at a risk-free rate. [Investopedia](https://www.investopedia.com/articles/investing/021015/advantages-and-disadvantages-capm-model.asp) mentions the same assumption and criticizes it as well:

> **Ability to Borrow at a Risk-Free Rate**  
> CAPM is built on four major assumptions, including one that reflects an unrealistic real-world picture. This assumption—that investors can borrow and lend at a risk-free rate—is unattainable in reality. Individual investors are unable to borrow (or lend) at the same rate as the U.S. government. Therefore, the minimum required return line might actually be less steep (provide a lower return) than the model calculates.

How big of a problem is that empirically? If it is not big, what mitigates it?

**Tags:** asset-pricing

---

## 1 answers

### Answer by username_1 on 2022-10-12. Score: 2

In the words of [Fama & French, The Capital Asset Pricing Model:
Theory and Evidence, Journal of Economic Perspectives—Volume 18, Number 3—Summer 2004—Pages 25–46](http://www-personal.umich.edu/%7Ekathrynd/JEP.FamaandFrench.pdf),

> The problems [of CAPM] are serious enough to invalidate most
> applications of the CAPM.
>
> The CAPM, like Markowitz’s (1952, 1959) portfolio model on which it is
> built, is nevertheless a theoretical tour de force. We continue to
> teach the CAPM as an introduction to the fundamental concepts of
> portfolio theory and asset pricing, to be built on by more complicated
> models like Merton’s (1973) ICAPM. But we also warn students that
> despite its seductive simplicity, the CAPM’s empirical problems
> probably invalidate its use in applications.

[Wikipedia](https://en.wikipedia.org/wiki/Capital_asset_pricing_model#Problems) offers a good collection of problems of the CAPM model. I honestly think that the risk free rate assumption is one of the smallest problems of the whole idea.

It is the second highest entry in the list of the most dangerous concepts in quantitative finance work on [Quantitative Finance SE](https://quant.stackexchange.com/a/157/54838), with correlation being the first one in the list. Since you compute beta using correlation...

That said, individual investors are not the major players and institutional investors can for example use REPOs with government bonds as collateral that trade in line with risk free rates. There are several similiar funding vehicles available.

> **Comments:**
> **username_0**: Thanks! Hillier et al. "Fundamentals of Corporate Finance: 4th European Edition" (2022) states in chapter 13 that CAPM is still very widely by companies for estimating cost of capital and is actually the most popular method for that purpose. So I guess it must be worth something. My question can be seen in that context.  
> **username_1**: One of the most widely cited problems with WACC is the use of beta. The benefit of CAPM is its simplicity and speed of computation. Also, what is an alternative? The Dividend Discount Model? Valuing companies based on spreadsheets of cashflows of some sorts or past prices is usually limited by design. In my experience, corporate finance, accounting/controlling is often very mechanical and follows simple rules. At least partly also because teams notoriously lack personnel, but also that results need to be communicated and explained to superiors. It's a safe bet to do what everyone else does.  

---

