<blockquote>
<p>Does the discounted dividend model assume a stock underperforms the risk-free rate?</p>
</blockquote>
<p>No, note <span class="math-container">$r$</span> is not risk free rate. In Gordon growth model (i.e. the model your equation describes) <span class="math-container">$r$</span> is the company's cost of capital/equity not the risk free rate. You can read about it straight from the horse's mouth in the <a href="https://sci-hub.se/https://www.tandfonline.com/doi/abs/10.2469/faj.v53.n3.2084" rel="nofollow noreferrer">Gordon &amp; Gordon 1997 paper</a>. Hence <span class="math-container">$r$</span> is the risk free rate plus whatever risk premium the company pays i.e. <span class="math-container">$r= r_f+r_i$</span> where <span class="math-container">$r_f$</span> is the risk free rate and <span class="math-container">$r_i$</span> the risk premium company pays over it.</p>
<p>As a consequence the formula does not say that investor cannot get higher return than risk free rate. Only, if you assume that <span class="math-container">$r=r_f$</span> that would be true.</p>
<p>Moreover, regular investors generally don't have option to invest into genuine risk free assets. Even US or Swiss bonds are just very close to be risk free but not completely risk free.</p>
<p>Maybe in class your professor used <span class="math-container">$r=r_f$</span> as a simplifying assumption, but that is clearly not something inherent to Gordon growth model and the <span class="math-container">$r$</span> in your formula will realistically be high above true risk free rate.</p>

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2024-01-17T17:22:40.823Z
2024-01-17T17:22:40.823Z
1muflon1
<p>I'm trying to understand intuitively why the stock market as a whole has outperforms the risk-free rate over time. I started by looking at the discounted dividend model which is one of the few things I remember from academic courses a long time ago.</p>
<p>Consider a stock that just paid a dividend <span class="math-container">$D$</span>. If we assume a constant discount rate <span class="math-container">$r$</span> and a constant growth rate <span class="math-container">$g$</span>, the discounted dividend model tells us that the present value of the stock should be</p>
<p><span class="math-container">$$
P=\frac{D(1+g)}{r-g}.
$$</span></p>
<p>The math behind how to get here is simple, but I'm wondering what this model even tells us. For the model to make sense we have to have <span class="math-container">$r&gt;g$</span>. But if that were true then why would you hold such a stock? Wouldn't it make more sense to continuously invest in the risk-free rate?</p>
<p>There must be something I'm missing. Any guidance or intuition is greatly appreciated.</p>

<interest-rate><finance><stock-market><financial-economics><efficient-markets>
Does the discounted dividend model assume a stock underperforms the risk-free rate?
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# Does the discounted dividend model assume a stock underperforms the risk-free rate?

(Asked by: username_0 on 2024-01-16)

I'm trying to understand intuitively why the stock market as a whole has outperforms the risk-free rate over time. I started by looking at the discounted dividend model which is one of the few things I remember from academic courses a long time ago.

Consider a stock that just paid a dividend $D$. If we assume a constant discount rate $r$ and a constant growth rate $g$, the discounted dividend model tells us that the present value of the stock should be

$$
P=\frac{D(1+g)}{r-g}.
$$

The math behind how to get here is simple, but I'm wondering what this model even tells us. For the model to make sense we have to have $r>g$. But if that were true then why would you hold such a stock? Wouldn't it make more sense to continuously invest in the risk-free rate?

There must be something I'm missing. Any guidance or intuition is greatly appreciated.

**Tags:** interest-rate, finance, stock-market, financial-economics, efficient-markets


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## 1 answers

### Answer by username_1 on 2024-01-17. Score: 1

> Does the discounted dividend model assume a stock underperforms the risk-free rate?

No, note $r$ is not risk free rate. In Gordon growth model (i.e. the model your equation describes) $r$ is the company's cost of capital/equity not the risk free rate. You can read about it straight from the horse's mouth in the [Gordon & Gordon 1997 paper](https://sci-hub.se/https://www.tandfonline.com/doi/abs/10.2469/faj.v53.n3.2084). Hence $r$ is the risk free rate plus whatever risk premium the company pays i.e. $r= r\_f+r\_i$ where $r\_f$ is the risk free rate and $r\_i$ the risk premium company pays over it.

As a consequence the formula does not say that investor cannot get higher return than risk free rate. Only, if you assume that $r=r\_f$ that would be true.

Moreover, regular investors generally don't have option to invest into genuine risk free assets. Even US or Swiss bonds are just very close to be risk free but not completely risk free.

Maybe in class your professor used $r=r\_f$ as a simplifying assumption, but that is clearly not something inherent to Gordon growth model and the $r$ in your formula will realistically be high above true risk free rate.


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