Rational, intelligent investors should not simply accept the fact that value investing works simply because it has been quite successful over the decades. Why should we buy “undervalued” assets and expect to sell them at “fair value” in the future? And what process, if any, causes the price to revert back to this “fair value”?

**In this article, James Miao tackles these problems by creatively applying economic principles.**

## Investor strategy and machine learning tools

Firstly, let’s define value investing as a strategy where the investor buys (sells) undervalued (overvalued) cash flow generating assets, especially equities, and holds the security until the market price reflects the true intrinsic value.

*Define the intrinsic value of a example company as the present value of all future cashflows, discounted at some rate (typically the weighted average cost of capital).*

This precise definition tells us that there is no difference between the traditional styles of “value” and “growth”. It doesn’t matter if you chase above-average growth or underpriced companies, because what really matters is the present value of the future cashflows. This idea fits in perfectly with Warren Buffet’s idea of “intrinsic value”.

*Define the observed or market value of the company as the latest tradeable market price.*

We can re-write the current market price in terms of implied cash flows discounted at the same rate as the intrinsic value. These implied cash flows are the market’s interpretation of future cash flows and we might account for these just like depreciation/amortisation, given their unreal nature.

*Define the estimated value of the company as an individual investor’s “best guess” at the intrinsic value of the company.*

This intrinsic value is not directly observable, but can be estimated. Investors might estimate the company’s value by performing fundamental analysis – taking in factors such as industry growth, competitors, and competitive advantage and so on. This resulting estimate is modelled as a random variable, reflecting the investor’s degree of uncertainty. Indeed, if the investor estimates the value incorrectly, he stands to lose a lot of money!

Crucially, we can expect that investors’ estimates of value are accurate on average, due to the statistical properties of measurement errors.

Now that we have dispensed with all the necessary definitions, we can now proceed to the argument.

Suppose we know* with certainty *that the intrinsic value of the company is higher than the observed value.

How can we profit from this difference? The only way to do this without risk is to buy the stock and keep receiving cashflows until the company ceases business – much like holding a bond to maturity.

The value of the profit today is the difference between the present values of all future actual and implied cash flows. Equivalently, profit = intrinsic value – market value.

## The arrows and the cash flows

This transaction is similar to a riskless arbitrage in that we have “bought” the real cashflows and hedged them for a profit by “selling” the implied, unreal cashflows for a cheaper price.

Assume that all investors have the same expectations, risk aversion, wealth, transaction costs and market access. Additionally, they all hold the same market portfolio (i.e. they all hold the ASX200 index), they reside in a tax regime that allows full franking of dividends and that they have infinite patience (i.e. they can hold their shares from now until the company goes bust).

An investor expects to gain a profit equal to the difference between the estimated value and the market value of the company. Note that the investor is infinitely patient, so this profit does not include any resale values – the investor is content to recoup his investment from dividends.

What is his risk? His risk is purely the uncertainty arising from estimating the intrinsic value. This is because we cannot predict the future with certainty, especially with limited public and perhaps private information. Note that there is no resale price risk because investors are assumed to hold shares till the cessation of the company.

The investor now considers his risk and expected profit and decides whether to buy the security. He will now only buy if the security offers a better risk adjusted return than his currently existing portfolio (ignore diversification benefit, as he already holds the market portfolio). For example, if the market portfolio has a risk adjusted return of 10% and the security offers 15%, then he will buy.

All investors, which we assume to be perfectly identical, will rush in to buy the security. This drives up the price until it reaches somewhere close to, but never at the estimated value.

## The price and risk: The trading software

In reality, prices don’t plateau like this – this result is due to our assumptions. This shouldn’t obscure the main idea that investors’ individual search for higher returns will increase demand and thus force the price to revert back to the estimated price. The trading software can help the investors and the value companies.

Now what happens when we relax some assumptions?

Remember that we assumed all investors have to hold shares until the company ceases operating? Due to the time value of money, the resale risk of the shares will become insignificant as time passes. Hence, the investor can hold the shares for a reasonable timeframe, say 5-10years, and still gain a profit approximately equal to the profit if held to the end of the company’s life. This approximation effect means that our argument remains valid.

Taking the axe to the assumption of **homogeneous expectations**, what happens if investors take different views of values? The path of the price as it reaches the estimated price is then determined by a tug-of-war between sellers and buyers.

At first, the undervalued asset has few sellers and many buyers. The law of demand and supply then pushes up the current price to the market’s average estimate of value, at which equilibrium is formed at the average estimate of value.

This process is a more accurate depiction of **the mechanism by which value investors** are able to cause prices to revert back to fair value (Remember that the market’s estimated value should be very close to the real intrinsic value on average).

Notice there is a “no man’s land” between the buyers and sellers due to the effect of the risk thresholds. Investors in this region will not buy or sell because the expected return from making a transaction is not worth the risk, thereby leaving a “power vacuum” in which prices may not be determined on the basis of value alone. After we relax the assumption of investors having homogenous risk aversion, it can be shown that traders such as momentum traders have ample opportunity to dictate the market’s movements.

Furthermore, the remaining assumptions can be removed without changing much of these mechanics. If we remove the assumption of equal wealth and use a highly skewed wealth distribution dominated by several large institutions, then the distribution of estimates will merely be more peaked at certain values. The introduction of trading costs only widens the “no man’s land” between buyers and sellers. Information asymmetry means that some investors will have less estimation risk than others, giving them an edge in the market. Since our argument remains strong even after the removal of all these assumptions, we should be reasonably confident that there is a sound fundamental reason behind the success of value investing.

Ultimately, the reason why value investment has worked for so long is human greed. Greed ensures that investors will always search for higher returns, adjusted for risk of course. This constant search for higher returns drives investors to compete for the best investment opportunities, which in turn drives up the price of undervalued assets back to their fundamental, intrinsic value.

So rest assured value investors, your investment approach will continue to be successful for as long as human greed exists.