# The difference between theoretical and market value

An important distinction in the financial markets is between the theoretical value and the market value of a financial instrument. In this article we will explain the difference and then discuss why it matters. We will also look at the difference uses of both types of value.

Any *liquid* financial asset that trades in a market has a current value. This is the** market value** and is simply the price at which the asset is trading. Economists will describe this as the *clearing* price which just means the price at which the supply and demand for the asset are currently matched. To know the market value of say Apple shares, we just look up the current price. This is pretty straightforward and generally not controversial; there is just one market value and it is simply the market price.

The **theoretical value** of an asset on the other hand is *not* such a straightforward affair. The theoretical value of an asset is the output of some sort of model. This could be a sophisticated mathematical model that takes a number of inputs to produce a single theoretical value. Or it could simply be an investor’s personal intuitive opinion about an asset’s value. That is still a model; it is just an implicit model in the investor’s own head! Notice that there can be an unlimited number of theoretical values. Different models and different people can each have their own idea of the theoretical value of an asset.

So why does this distinction matter to investors or traders? The distinction is crucial because it is the *difference* between the market and theoretical value, as each trader sees it, that drives a lot of the trading that occurs. The buyer of a financial asset will generally expect the price of the asset to rise; that’s why he is buying! Another way to understand this is to say that the buyer thinks the market value is *too low* compared to his theoretical value. He expects that the market value will rise to reflect the under-valuation.

Consider professional option traders. They will typically have theoretical values for all the option contracts they are trading. These will be the output of a mathematical model which takes into account various factors such as the spot price, time to expiry, implied volatility etc. Now when the trader sees an option trading at a price that is *different* to his theoretical value (i.e the market value is different from his theoretical value), he needs to decide whether he thinks the market value is ‘wrong’ or his theoretical value is ‘wrong’. It is not possible for one asset to have two values at the same time! As the trader sees more activity in the market in this and related option contracts, he should be able to gauge whether it is his model that needs alteration or whether there is indeed some ‘edge’ in the market (i.e. profit to be made).

## The importance of the distinction between theoretical and market value for risk

For risk management, the theoretical vs market distinction is important. For example, when measuring the profit and loss of a portfolio, should the risk manager use the current market value of the assets or some sort of theoretical value? In practice, risk managers will tend to use both values and therefore to have *two* profit and losses. The market value is indisputable and reflects the real, *actual* profit and loss. But the theoretical value is after all what the trader or bank must have some faith in otherwise they are trading using models they don’t believe in!

It is not just the *value* of an asset that can be actual or theoretical Many different parameters which feed into the risk numbers could be theoretical or market-based. For example, option traders will typically use a *theoretical* level of implied volatility for their options although they could use the market value. The outputs from the risk models (as opposed to their pricing models) will also therefore be dependent on whether market or theoretical values are used. This could mean that, for example, a trader’s portfolio delta might be different depending on whether he uses the theoretical or market levels of implied volatility.

In short then, it is not just the profit and loss that can have two interpretations (market vs theoretical). Risk metrics as well can be fully dependent on whether market or theoretical values of other parameters are used.

In Volcube simulations, you typically trade using theoretical option values and the market values are determined by the order flow in the market. Although if you prefer, you can just trade using the market values.

## Aligning theoretical and market values

Sometimes traders decide to alter their theoretical values, usually because they want to more accurately reflect the market value. If a trader values an asset at x but the market consistently values the asset at y, eventually the trader may feel he needs to move his value closer to y. There are several reasons for this; as mentioned above it is not just the profit and loss that is a function of the type of value used, but also the risk metrics which can be affected by the value. If the trader’s theoretical values are ‘wrong’, then his risk management and hedging strategies will also be based on ‘wrong’ computations. So this is one reason to decide to re-align theoretical values.

Option traders will typically use a ‘volatility manager’ to change the implied volatility they are using and thus align theoretical and market values. You can practise this as well in Volcube simulations by using the Volcube volatility manager.

It is important to understand the difference between the theoretical and market value of any financial asset, particularly when reviewing trading results. Theoretical value can be an important guide, but remember it is the market value which determines the dollars, pounds and euros that will be sitting in the trader’s bank account when all is said and done!

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*"Using Volcube Starter Edition, I can learn about more than just the theory of options; I can learn about **trading* options. The options market simulator is a fantastic way to learn, simple to use and a lot of fun! The videos and articles are comprehensive and easy to understand, and the Volcube Team offers you excellent support whenever you need it. Highly recommended.”

*"Using Volcube Starter Edition, I can learn about more than just the theory of options; I can learn about*

*trading*options. The options market simulator is a fantastic way to learn, simple to use and a lot of fun! The videos and articles are comprehensive and easy to understand, and the Volcube Team offers you excellent support whenever you need it. Highly recommended.”**Andrew Kang**

BA Economics, Northwestern University

& Trainee derivatives trader in Chicago