<p>$
\newcommand{\Cov}{\text{Cov}}
$</p>

<blockquote>
  <ul>
  <li>Why can the $\beta_{asset}$ be seen as if the firm had been financed only with equity?</li>
  </ul>
</blockquote>

<p>The general idea with regard to this question stems from a discussion about how equity is a residual claim. To go through this step-by-step, recall that the value of a firm is given by the discounted present value of its cash flows. Equity is a claim to whatever is left over after other financial claim-holders have been paid (e.g., debt).  In this way, equity can be viewed as a call option and debt can be viewed as a put option. (See <a href="http://pages.stern.nyu.edu/~adamodar/New_Home_Page/lectures/opt.html" rel="nofollow noreferrer">here</a> and <a href="http://nitinranahome.blogspot.com/2013/02/debt-and-equity-valuation-using-option.html" rel="nofollow noreferrer">here</a>.)</p>

<p>So, if the firm was financed only by equity, then equity would be the claim to 100% of the cash flow. Thus, $\beta_{\text{asset}}$ in that case can be seen as the if the firm was only financed with equity.</p>

<blockquote>
  <ul>
  <li>We can measure the $\beta_{equity}$ by CAPM, but how can we measure $\beta_{debt}$?</li>
  </ul>
</blockquote>

<p>You say that you can measure $\beta_{\text{equity}}$ by CAPM. However, you can measure any cash-flow by CAPM---even debt. Since $V = D + E$, keep in mind that
$$
\Cov(X + Y, Z) = \Cov(X,Z) + \Cov(Y,Z).
$$
The problem, I guess, is that you need to know the distribution of debts cash flows. This depends on the face value of total debt and the distribution of the underlying cash flows. This can get especially complicated if you're thinking about considering a dynamic setting. </p>

<p>This question, I'm guessing, came from a discussion of the Modigliani-Miller theorem. Remember the idea behind Proposition 2. It's illustrated in the following graph:
<a href="https://i.sstatic.net/owphI.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/owphI.png" alt="enter image description here"></a></p>

CC BY-SA 3.0
2016-02-13T20:41:45.800Z
2016-02-13T20:41:45.800Z
jmbejara
<p>Usually Beta of debt is hard to find and is assumed to be zero however it's not actually zero as we do have a bond market and it certainly fluctuates but not like equity markets. We compute asset beta to know what beta company would have if it's all equity financed and then compare it with it's peers and take a average of it. Once we have an average then we could do the reverse calculation and find equity beta for the company. Now why we do this because Beta has to capture industry and company specific risk and should be free of non systematic risk. Hence once we have that we can compute company specific risk by computing gearing ratio.</p>

<p>Hope this answers your query.</p>

CC BY-SA 3.0
2015-08-19T11:56:17.683Z
Thanks for your answer. Could you please elaborate further on your first sentence(why isn't the bond market like the equity market?), and on your last sentence(what's gearing ratio, and how does it help in computing company specific risk? )
An old man in the sea.
CC BY-SA 3.0
2015-08-17T13:18:07.640Z
2015-08-17T13:18:07.640Z
manish
<p>My question is related to the following equation:
$$\beta_{asset}=\frac{Equity}{Equity+Debt}\beta_{equity}+\frac{Debt}{Equity+Debt}\beta_{debt} $$</p>

<ul>
<li>Why can the $\beta_{asset}$ be seen as if the firm had been financed only with equity?</li>
<li>We can measure the $\beta_{equity}$ by CAPM, but how can we measure $\beta_{debt}$?</li>
</ul>

<p>Any help would be appreciated</p>

CC BY-SA 3.0
2015-08-13T18:00:03.547Z
I don't understand the first bullet?
AnilB
CC BY-SA 3.0
2015-08-14T08:10:48.993Z
@OccupyGezi  the book states «the asset beta could also be thought of as the beta of the firm's shares had the firm been financed only with equity». 
lol I think I now get the first bullet. What they mean is that if the firm has no debt, then the asset beta = equity beta, right?
An old man in the sea.
CC BY-SA 3.0
2015-08-14T08:59:47.420Z
Yes exactly....
AnilB
CC BY-SA 3.0
2015-08-14T13:03:03.957Z
@OccupyGezi what about the second bullet?
An old man in the sea.
<corporate-finance>
Firms Betas - Equity, Debt betas
An old man in the sea.
# Firms Betas - Equity, Debt betas

(Asked by: username_0 on 2015-08-13)

My question is related to the following equation:
$$\beta\_{asset}=\frac{Equity}{Equity+Debt}\beta\_{equity}+\frac{Debt}{Equity+Debt}\beta\_{debt} $$

* Why can the $\beta\_{asset}$ be seen as if the firm had been financed only with equity?
* We can measure the $\beta\_{equity}$ by CAPM, but how can we measure $\beta\_{debt}$?

Any help would be appreciated

**Tags:** corporate-finance

> **Comments:**
> **username_1**: I don't understand the first bullet?  
> **username_0**: @OccupyGezi  the book states «the asset beta could also be thought of as the beta of the firm's shares had the firm been financed only with equity».  lol I think I now get the first bullet. What they mean is that if the firm has no debt, then the asset beta = equity beta, right?  
> **username_1**: Yes exactly....  
> **username_0**: @OccupyGezi what about the second bullet?  

---

## 2 answers

### Answer by username_2 on 2016-02-13. Score: 1

$
\newcommand{\Cov}{\text{Cov}}
$

> * Why can the $\beta\_{asset}$ be seen as if the firm had been financed only with equity?

The general idea with regard to this question stems from a discussion about how equity is a residual claim. To go through this step-by-step, recall that the value of a firm is given by the discounted present value of its cash flows. Equity is a claim to whatever is left over after other financial claim-holders have been paid (e.g., debt). In this way, equity can be viewed as a call option and debt can be viewed as a put option. (See [here](http://pages.stern.nyu.edu/~adamodar/New_Home_Page/lectures/opt.html) and [here](http://nitinranahome.blogspot.com/2013/02/debt-and-equity-valuation-using-option.html).)

So, if the firm was financed only by equity, then equity would be the claim to 100% of the cash flow. Thus, $\beta\_{\text{asset}}$ in that case can be seen as the if the firm was only financed with equity.

> * We can measure the $\beta\_{equity}$ by CAPM, but how can we measure $\beta\_{debt}$?

You say that you can measure $\beta\_{\text{equity}}$ by CAPM. However, you can measure any cash-flow by CAPM---even debt. Since $V = D + E$, keep in mind that
$$
\Cov(X + Y, Z) = \Cov(X,Z) + \Cov(Y,Z).
$$
The problem, I guess, is that you need to know the distribution of debts cash flows. This depends on the face value of total debt and the distribution of the underlying cash flows. This can get especially complicated if you're thinking about considering a dynamic setting.

This question, I'm guessing, came from a discussion of the Modigliani-Miller theorem. Remember the idea behind Proposition 2. It's illustrated in the following graph:
[![enter image description here](https://i.sstatic.net/owphI.png)](https://i.sstatic.net/owphI.png)


---

### Answer by username_3 on 2015-08-17. Score: 0

Usually Beta of debt is hard to find and is assumed to be zero however it's not actually zero as we do have a bond market and it certainly fluctuates but not like equity markets. We compute asset beta to know what beta company would have if it's all equity financed and then compare it with it's peers and take a average of it. Once we have an average then we could do the reverse calculation and find equity beta for the company. Now why we do this because Beta has to capture industry and company specific risk and should be free of non systematic risk. Hence once we have that we can compute company specific risk by computing gearing ratio.

Hope this answers your query.

> **Comments:**
> **username_0**: Thanks for your answer. Could you please elaborate further on your first sentence(why isn't the bond market like the equity market?), and on your last sentence(what's gearing ratio, and how does it help in computing company specific risk? )  

---

