# How to understand share value vs real worth of the company

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 .

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 of a 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 (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.

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.

• Under the assumption of efficient markets, markets uncover the fundamental value (i.e. "real worth") of assets by trading them. Continuing this line of argument to the logical extreme, the sum of a company's marked-to-market liabilities must equal its fundamental value. – user7935 Sep 9 '16 at 12:51
• @Timo no, because there is no perfect knowledge of the future. – EnergyNumbers Sep 9 '16 at 13:21
• You don't need to have perfect knowledge of the future to determine the value of something. For example, you can valuate a gamble on a coin flip without knowing beforehand if it's going to come up heads or tails. This is because you know the distribution of outcomes and their associated payoffs. You don't need to know the exact cash flow structure in advance. An efficient market does the same thing for any financial asset (although of course you only observe the price, not the underlying distribution and associated payoff structure). – user7935 Sep 10 '16 at 20:17
• @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. – EnergyNumbers Sep 11 '16 at 0:08
• I'm not familiar with the definition of an efficient market as one that does not uncover the true value of assets. Do you perhaps have recommendations for readings that use this definition? – user7935 Sep 12 '16 at 8:35