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Forward rates are interest rates that can be taken in advance using the term structure.

Â I was writing an article about the term structure of interest rates and I was wondering,

Â "Who invented the concept of forward rate?"

Â And I couldn't figure it out.

Â It's hard to find the first

Â especially back when I was writing when we didn't have the internet.

Â I asked a graduate student,

Â "Can you find out who invented the concept of forward rate?

Â I think it's Sir John Hicks.".

Â So my graduate student went to the library,

Â -the way we used to do these things- and tried to find out.

Â Then he came back to me and he said, "You know,

Â Sir John Hicks is still alive,

Â you could ask Him."

Â So I thought, "I never thought of that.

Â Is he still alive?"

Â So this is back.

Â I don't know like 1980 or something.

Â So I thought, "All right, I'll find his address and I'll mail him a letter."

Â So I typed a letter to him saying,

Â "Did you invent the concept of forward rates?"

Â And I waited about six months and then I get a letter back

Â handwritten with shaky handwriting and so John Hicks said, "Interesting question.

Â Did I invent that concept?"

Â He had shaky handwriting, "I apologize,

Â my health is not good anymore,

Â but I thought I would answer your question."

Â So he went back and he said,

Â "Well, I thought it was,

Â I did a trans- my wife and I did a translation around

Â 1920 of a book by a Swedish economist.

Â I thought it was there,

Â but I went and it's not there."

Â And then he said, he reminisced about conversations he had at

Â coffee hour at the London School of Economics in the 1920s and he said,

Â "Well, maybe somebody brought this up,

Â but I don't know.

Â Maybe I didn't read it."

Â So I put my example here at the coffee hour at the London School of Economics.

Â The year is 1925.

Â This assumes that he got it from some verbal conversation but nobody knows.

Â He's long gone now,

Â we can't ask him again.

Â So here we are sitting at the London School of Economics in 1925 and somebody is saying,

Â "I'm wondering what interest rates I can invest money at in 1926?"

Â That's next year. Remember you got to put yourself back in the time machine here.

Â So the year is 1925 and you want to invest the money between 1926 and 1927.

Â And he said, "I just wonder what interest rate I can get in 1926?"

Â That's a year in the future.

Â But apparently somebody maybe it was Sir John Hicks at the coffee hour said,

Â "That's a dumb question."

Â Maybe he wasn't so rude.

Â He said, "I can get it today.

Â I can lock it in today."

Â This is 1925, but there's already an interest rate between 1926 and 1927.

Â So we'll call that the forward rate,

Â but that term hadn't been invented.

Â It's amazing how simple concepts don't seem to be known

Â until somebody points them out aggressively.

Â So this is the coffee hour conversation as I'm reconstructing it.

Â This is how you do it.

Â How do I lock in an interest rate as an investor from 1926 to 1927?

Â I buy in 1925,

Â this number of two-period discount bonds maturing at 100 pounds in 1927.

Â They are two-year bonds.

Â The cost- okay.

Â So, I'm buying this number of them.

Â So if I'm buying this number of them,

Â the cost to me is one pound over one plus r one.

Â And then I have to short in 1925 one- one period discount bond maturing at $100 in 1926.

Â So I receive one over one plus r one pounds.

Â Now think about it.

Â I have locked in an interest rate equal one plus F which is equal to one plus this

Â two- period yield-to-maturity squared all over

Â one plus the one period you have to maturity. And I've locked it in.

Â So this was kind of a showstopper at the coffee hour at the LLC in 1925.

Â This guy thought he was answering unanswerable question and here it is.

Â So that you could pick up today's copy of

Â the London Times and these prices of discount bonds will be listed.

Â I can tell you exactly what the market today is quoting for the 1926 to 1927 investment.

Â So is that- is that clear?

Â It's a little tricky I guess nobody thought to talk in those terms until then.

Â