<p>When a stock price changes, it implies that the present value of future cash flows from the company to investors has changed.</p>

<p>A multitude of different things can change that number, and ascertaining <em>why</em> a stock price changed is often difficult or near impossible.</p>

<h3>Simple example: one period cash flow, no uncertainty</h3>

<p>Let $r^f$ be the risk free rate. Let $c$ be some cash flow one period ahead.</p>

<p>The present value of the cash flow is:</p>

<p>$$ p = \frac{1}{1+r^f} c$$ And that's what it would trade for in efficient market. Two key observations:</p>

<ol>
<li>If the discount rate $\frac{1}{1 + r^f}$ were different, then the price would be different.</li>
<li>If the future cash flow $c$ were different, the price would also be different.</li>
</ol>

<p>Conceptually, the price of a financial asset can be decomposed into some discount rate times the quantity of a future cash flow.</p>

<h3>More complicated setup, one period cash flow, uncertainty</h3>

<p>With the addition of uncertainty, you get a conceptually similar result: the price of a financial asset should be the <a href="http://mathworld.wolfram.com/InnerProduct.html" rel="nofollow">inner product</a> of a <a href="https://en.wikipedia.org/wiki/Stochastic_discount_factor" rel="nofollow">discount factor</a> with the future cash flow. Let $\mathbf{s}$ be a random variable denoting the stochastic discount factor, and let $\mathbf{c}$ be a random variable denoting the future cash flow. The <a href="https://en.wikipedia.org/wiki/Law_of_one_price" rel="nofollow">Law of One Price</a> (LOOP) implies the existence of a stochastic discount factor $\mathbf{s}$ such that:</p>

<p>$$ p = E[\mathbf{s}\cdot\mathbf{c}] $$</p>

<p>Let $\mathcal{F}_t$ be the set of information available at time $t$. As new information becomes available, the conditional expectation will change:</p>

<p>$$ p_t = E\left[\left. \mathbf{s}\cdot \mathbf{c} \, \right| \, \mathcal{F}_t \right] $$</p>

<p>This looks fancy, but it's almost the <em>same</em> idea as the simple, one period cash flow case. The price of an asset today is the product of a discount factor and future cash flows. <strong>In an efficient market, changes in asset prices may be due to news about discount rates or news about cash flows!</strong></p>

<p>If the share price triples, that's almost certainly due to positive news about future cash flows. Small changes though, or changes at the level of the overall S&amp;P500 index are trickier.</p>

<h3>Practical Implications</h3>

<p>In the fall of 2008, the stock market collapsed! Asset prices fell. What did this mean though? The decline may have be due to declining expectations of future cash flows from the corporate sector. <em>But</em> it also may have been due to rising discount rates, that risky future cash flows were being assigned a lower price! In a strict sense, disentangling discount rate news from cash flow news is nearly impossible. In general though, when looking at an individual company, you're almost certainly seeing more variation due to cash flow news than discount rate news, but strictly speaking, there's no way to make a clean decomposition.</p>

<h3>Sensitivity of the current price to future cash flow news...</h3>

<p>A number of features can make the price very sensitive to news:</p>

<ul>
<li>Leverage: If a company has a lot of debt and is near bankruptcy, the cash flows to equity may be massively different depending on whether the company survives or not.</li>
<li>Time horizon: How much is something like Uber worth? Will it take over global transportation with robotic, AI vehicles? Or will it sink under a morass of rising labor costs and government regulation? The big payoffs from something like Uber are in the distant future, and forecasts of the distant future may be volatile, sensitive to certain types of news.</li>
</ul>

CC BY-SA 3.0
2016-09-09T19:32:54.577Z
2016-09-10T06:16:31.183Z
2016-09-10T06:16:31.183Z
Matthew Gunn
<p>No one knows what the "real worth" of a company is. One could consider it to be be equal to the net present value of all its future cashflows. But no one knows what those cashflows will be, so its "real worth" is unknowable.</p>

<p>If the market is efficient, then the market capitalisation of the company (share price multiplied by number of shares) represents the market's best guess at what that real worth is. That is to say, it reflects the market's averaged expectation of all future cashflows, discounted to today.</p>

<p>So if a company's share price doubles, without any change in the number of shares issued, then the market is saying that it expects the net present value of all the company's future cashflows to have doubled.</p>

CC BY-SA 3.0
2016-09-09T13:21:29.207Z
@Timo no, because there is no perfect knowledge of the future.
410 gone
CC BY-SA 3.0
2016-09-11T00:08:22.057Z
@Timo that's exactly the point: no one knows the future underlying distribution, nor the future payoff structure. Hence "real worth" is unknowable. Efficient markets do not uncover the "fundamental value", because such a thing is impossible. Instead, they offer, on average, potential reward that is commensurate with the potential risk, and that's a completely different thing.
410 gone
CC BY-SA 3.0
2016-09-09T06:49:38.873Z
2016-09-09T06:49:38.873Z
410 gone
<p>When read in the news articles for stock market price, I learned that the share value of a company changes in a year.  My question is does the share value really reflect if the company is doing good or not?</p>

<p>Example: In the recent aPIGEE article it says,  the company in a 52 week duration share value ranged from \$5.45 to \$16.34 .</p>

<stock-market>
How to understand share value vs real worth of the company
cnacy
# How to understand share value vs real worth of the company

(Asked by: username_0 on 2016-09-09)

When read in the news articles for stock market price, I learned that the share value of a company changes in a year. My question is does the share value really reflect if the company is doing good or not?

Example: In the recent aPIGEE article it says, the company in a 52 week duration share value ranged from \$5.45 to \$16.34 .

**Tags:** stock-market

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## 2 answers

### Answer by username_1 on 2016-09-09. Score: 2

When a stock price changes, it implies that the present value of future cash flows from the company to investors has changed.

A multitude of different things can change that number, and ascertaining *why* a stock price changed is often difficult or near impossible.

### Simple example: one period cash flow, no uncertainty

Let $r^f$ be the risk free rate. Let $c$ be some cash flow one period ahead.

The present value of the cash flow is:

$$ p = \frac{1}{1+r^f} c$$ And that's what it would trade for in efficient market. Two key observations:

1. If the discount rate $\frac{1}{1 + r^f}$ were different, then the price would be different.
2. If the future cash flow $c$ were different, the price would also be different.

Conceptually, the price of a financial asset can be decomposed into some discount rate times the quantity of a future cash flow.

### More complicated setup, one period cash flow, uncertainty

With the addition of uncertainty, you get a conceptually similar result: the price of a financial asset should be the [inner product](http://mathworld.wolfram.com/InnerProduct.html) of a [discount factor](https://en.wikipedia.org/wiki/Stochastic_discount_factor) with the future cash flow. Let $\mathbf{s}$ be a random variable denoting the stochastic discount factor, and let $\mathbf{c}$ be a random variable denoting the future cash flow. The [Law of One Price](https://en.wikipedia.org/wiki/Law_of_one_price) (LOOP) implies the existence of a stochastic discount factor $\mathbf{s}$ such that:

$$ p = E[\mathbf{s}\cdot\mathbf{c}] $$

Let $\mathcal{F}\_t$ be the set of information available at time $t$. As new information becomes available, the conditional expectation will change:

$$ p\_t = E\left[\left. \mathbf{s}\cdot \mathbf{c} \, \right| \, \mathcal{F}\_t \right] $$

This looks fancy, but it's almost the *same* idea as the simple, one period cash flow case. The price of an asset today is the product of a discount factor and future cash flows. **In an efficient market, changes in asset prices may be due to news about discount rates or news about cash flows!**

If the share price triples, that's almost certainly due to positive news about future cash flows. Small changes though, or changes at the level of the overall S&P500 index are trickier.

### Practical Implications

In the fall of 2008, the stock market collapsed! Asset prices fell. What did this mean though? The decline may have be due to declining expectations of future cash flows from the corporate sector. *But* it also may have been due to rising discount rates, that risky future cash flows were being assigned a lower price! In a strict sense, disentangling discount rate news from cash flow news is nearly impossible. In general though, when looking at an individual company, you're almost certainly seeing more variation due to cash flow news than discount rate news, but strictly speaking, there's no way to make a clean decomposition.

### Sensitivity of the current price to future cash flow news...

A number of features can make the price very sensitive to news:

* Leverage: If a company has a lot of debt and is near bankruptcy, the cash flows to equity may be massively different depending on whether the company survives or not.
* Time horizon: How much is something like Uber worth? Will it take over global transportation with robotic, AI vehicles? Or will it sink under a morass of rising labor costs and government regulation? The big payoffs from something like Uber are in the distant future, and forecasts of the distant future may be volatile, sensitive to certain types of news.


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### Answer by username_2 on 2016-09-09. Score: 1

No one knows what the "real worth" of a company is. One could consider it to be be equal to the net present value of all its future cashflows. But no one knows what those cashflows will be, so its "real worth" is unknowable.

If the market is efficient, then the market capitalisation of the company (share price multiplied by number of shares) represents the market's best guess at what that real worth is. That is to say, it reflects the market's averaged expectation of all future cashflows, discounted to today.

So if a company's share price doubles, without any change in the number of shares issued, then the market is saying that it expects the net present value of all the company's future cashflows to have doubled.

> **Comments:**
> **username_2**: @Timo no, because there is no perfect knowledge of the future.  
> **username_2**: @Timo that's exactly the point: no one knows the future underlying distribution, nor the future payoff structure. Hence "real worth" is unknowable. Efficient markets do not uncover the "fundamental value", because such a thing is impossible. Instead, they offer, on average, potential reward that is commensurate with the potential risk, and that's a completely different thing.  

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