Forward rates are interest rates that can be taken in advance using the term structure. I was writing an article about the term structure of interest rates and I was wondering, "Who invented the concept of forward rate?" And I couldn't figure it out. It's hard to find the first especially back when I was writing when we didn't have the internet. I asked a graduate student, "Can you find out who invented the concept of forward rate? I think it's Sir John Hicks.". So my graduate student went to the library, -the way we used to do these things- and tried to find out. Then he came back to me and he said, "You know, Sir John Hicks is still alive, you could ask Him." So I thought, "I never thought of that. Is he still alive?" So this is back. I don't know like 1980 or something. So I thought, "All right, I'll find his address and I'll mail him a letter." So I typed a letter to him saying, "Did you invent the concept of forward rates?" And I waited about six months and then I get a letter back handwritten with shaky handwriting and so John Hicks said, "Interesting question. Did I invent that concept?" He had shaky handwriting, "I apologize, my health is not good anymore, but I thought I would answer your question." So he went back and he said, "Well, I thought it was, I did a trans- my wife and I did a translation around 1920 of a book by a Swedish economist. I thought it was there, but I went and it's not there." And then he said, he reminisced about conversations he had at coffee hour at the London School of Economics in the 1920s and he said, "Well, maybe somebody brought this up, but I don't know. Maybe I didn't read it." So I put my example here at the coffee hour at the London School of Economics. The year is 1925. This assumes that he got it from some verbal conversation but nobody knows. He's long gone now, we can't ask him again. So here we are sitting at the London School of Economics in 1925 and somebody is saying, "I'm wondering what interest rates I can invest money at in 1926?" That's next year. Remember you got to put yourself back in the time machine here. So the year is 1925 and you want to invest the money between 1926 and 1927. And he said, "I just wonder what interest rate I can get in 1926?" That's a year in the future. But apparently somebody maybe it was Sir John Hicks at the coffee hour said, "That's a dumb question." Maybe he wasn't so rude. He said, "I can get it today. I can lock it in today." This is 1925, but there's already an interest rate between 1926 and 1927. So we'll call that the forward rate, but that term hadn't been invented. It's amazing how simple concepts don't seem to be known until somebody points them out aggressively. So this is the coffee hour conversation as I'm reconstructing it. This is how you do it. How do I lock in an interest rate as an investor from 1926 to 1927? I buy in 1925, this number of two-period discount bonds maturing at 100 pounds in 1927. They are two-year bonds. The cost- okay. So, I'm buying this number of them. So if I'm buying this number of them, the cost to me is one pound over one plus r one. And then I have to short in 1925 one- one period discount bond maturing at $100 in 1926. So I receive one over one plus r one pounds. Now think about it. I have locked in an interest rate equal one plus F which is equal to one plus this two- period yield-to-maturity squared all over one plus the one period you have to maturity. And I've locked it in. So this was kind of a showstopper at the coffee hour at the LLC in 1925. This guy thought he was answering unanswerable question and here it is. So that you could pick up today's copy of the London Times and these prices of discount bonds will be listed. I can tell you exactly what the market today is quoting for the 1926 to 1927 investment. So is that- is that clear? It's a little tricky I guess nobody thought to talk in those terms until then.
