# Can changes in the value of money be measured via interest rates and future contracts?

For most goods, we can compare the value of them by how people trade them. If in a free market, 10 apples can be traded for 20 oranges, then apples are twice as valuable as oranges. Likewise, if 10 apples can be traded for \$1, and 20 oranges can be traded for \$1, the same thing holds.

When I lend or borrow money, I am essentially buying or selling future money. If Alice lends Bob \$10 for 10 years with \$1 interest, then Bob is essentially selling Alice \$11 future dollars for a price of \$10 today. Additionally, if Bob buys \$10 of future corn today, and then corn is \$11 in the future, that means \$10 of todays money is worth \$10 of future money (on average since future corn today may be evaluated differently then future corn in the future, just due to unknown information. The free market is pretty smart in the long run though.)

Can this be used to track the changing value of money then, such as inflation and deflation?

(I guess its hard to use this, since both interest rates and the money supply are simultaneously manipulated by government backed institutions.)

Yes, but...

In theory what you suggest is pretty standard text book, and in fact Keynes makes exactly this point in his book The General Theory of Employment, Interest and Money as a way of getting a grip on the idea of interest and "Time-Value of Money" (don't have copy to hand, will update reference when I get a moment).

The problems come, as always, in the details - in fact in details that you have glossed over in your original set up.

If these 10 apples can be traded for those 20 oranges, then how can you be sure that another 10 apples can also be traded for a different 20 oranges. Or even, are we sure 100 apples can be traded for 200 oranges?

Adding the dimension of time to this, creates even more problems, but putting those aside the relationship you are looking for is

$$F=S_0e^{rT}$$

That is the future price ($F$) is equal to the price now ($S_0$), inflated by the time value of money.

Now back to apples and oranges. Are we certain that 10 apples now is the same as 10 apples in the future? Or more pertinently does the 10:20 apple:orange exchange rate persist into the future? Probably not.

Apples and oranges are both seasonal, and also suffer seasonal demand. We could image that apples are easy to come by now, but hard to get in 6 months time, vs oranges. Since you can't store them, this has to be reflected in the futures price. This means you will get a different $e^{rT}$ value for apples and oranges

These main causes of these difference are usually broken down thus

• Storage costs: can the thing be stored and delivered at the future date? If so how much does it cost to store?
• Carry: How much do you earn holding the thing for longer
• Convenience yield: How much premium are you willing to pay for the convenience of having it to hand?
• Credit risk: How much do you trust that the person will deliver (to the best of my knowledge there are no apple or orange futures, so we would be talking about a forward contract)

Take all these into account, and you have a commodity implied measure of future inflation. Of course, inflation as usually considered also includes services and retail products, on which there are very few (no?) futures/forwards. If you could find iPad futures and child care futures, then you would in theory be there.

For interest rates, the theory(spelled out as the Fisher equation) is that there are two components to the nominal interest rate. These are the real interest rate and the expected inflation. The real interest rate codifies the economy's 'urgency' or time preference: the idea that you prefer consuming now than tomorrow and so you need to be compensated for postponing your consumption. The expected inflation part is the one that compensates you for the change in prices between now and the future. In the data, these can be calculated from the differences in the yields of inflation-adjusted government bonds (TIPS) and traditional government bonds (Treasuries).

For futures, the basic idea is that the price (F) in a commodity future contract is indeed sort of the market's guess of the price of the commodity in the future. It would seem like the current spot price (S) is lower (higher) than F, then markets expect an increase (decrease) in the price of that commodity.

But this is not the only thing going on. For example, in times when producers would like to insure against changes in the price of their output, they will be willing to contract at a lower price than what they expect in the future. Similarly, when consumers would like to insure against changes in the price of their inputs, they will be willing to contract at a higher price than the one they expect in the future.

Typically you'd expect speculators that see a futures price that looks like it's below the expected spot price to enter into the futures contracts, hold on to them and then deliver the commodity to the spot market when the contract expires.

The difference between the current spot price and the futures price then is limited by the ability of producers to store their product, the ability of speculators, consumers and producers to absorb the risks, and so on. (The factors mentioned by @Corone)