Explaining Risk Premium
The purpose of this article is to simply explain to readers what a risk premium is and how it effects asset prices. I’m posting this because it is a very important concept for understanding the economy that I will need to reference in future posts when commenting on current events. The video below does a good job introducing the concept, but you may skip it if you’d like as a more precise explanation will follow.
Risk premium is an incredibly important concept in conceptualizing asset prices and understanding finance. In essence the risk premium is the additional payment an individual requires to compensate them for holding (or purchasing) an asset (or good) whose future value is uncertain.
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If it helps we can think of the difference between a bond and a stock. If an investor buys $100 of a bond yielding 5% annually in one year they are guaranteed to have $105 . If an investor buys $100 worth of stock the future price (the value to the investor) of the stock is uncertain. To compensate for this uncertainty the investor will demand a higher return (or compensation) for holding the stock.
Now of course the investor doesn’t know the true future value of the stock, but what they do have are expectations about what possibilities that price (value) might be. If the investor expects that the stock value will never be above $105, then they should always purchase a bond because they know that this guarantees them $105 . The concept of risk premium denotes the price (which will always be above $105) that an investor will need to expect in order to take the gamble and hold a stock instead of a bond.
We can express it mathematically as follows:
With asset 1 being the bond and asset 2 is the stock. R1 and R2 are the returns for each. T=x expresses that this is the value at some future time “x”, and the E expressing the fact that the value of the stock at T=x is only an expectation (its true value is uncertain). What this equation tells us is that if we assume the asset values are equal to the investment ($100), then the compensation for the uncertain payout of the stock will have to be greater than the return for the bond by a certain amount:
The actual expected value that the stock must be expected to attain in the future, in order to compensate for the risk, will vary based on the individual preference for risk. But it will always have to be greater than the sure thing.
The importance of this concept is paramount when understanding trade, finance, and the price of any asset. This is because prices will change constantly in the market place, and so the price one initially pays always has the possibility to vary in the future. This aspect of pricing inevitably leads to asset price bubbles. In paradoxical manner: as the future is always uncertain, and as prices increase so does uncertainty about true and expected value (in the same moment just as uncertainty increases so too do prices). If you can wrap your head around all these concepts and the previous paradox, you will have understand quite a bit about how finance works, bubbles; and how people make money with information, risk, and rising and falling prices.
Note: Models of risk and asset pricing can get very complicated but understanding this basic concept probably gives you 90% of the information needed to understand the bulk of whats actually important in the literature and reality.