What is spot rate?

Hey guys, it's William Jiamin here. In this video, I want to talk about a concept called spot rate. So, let's draw an example to explain it.

We have two individuals, A and B. A wants to borrow 100 units from B, and B agrees but wants it returned in one year. A suggests that they should pay back the exact amount borrowed, but B thinks there should be some gain from the transaction. B suggests that A should pay back more than 100 units in the future. However, A doesn't have that much money, so they agree that A will pay back the full 100 units in one year.

To analyze this transaction, let's consider it as an investment. B is investing 90 units and will receive 100 units in one year. The return on investment can be calculated by dividing the amount received by the amount invested, which gives us a return of approximately 11.11%.

Now, let's look at it from A's perspective. A is issuing a bond with a face value of 100 units, which doesn't require any interest or coupon payments during the one-year period. In one year, A will pay back the 100 units to the bond holder, which is B in this case.

At the time of issuing the bond, A only receives 90 units from B, which is the amount B invested. However, in one year, A needs to pay back the full face value of 100 units to the bond holder, which is B.

So, to calculate the spot rate, we divide the face value of the bond by the discount factor. In this case, since it's a one-year bond, we divide 100 by the discount factor to get the spot rate, which is denoted as n. This spot rate can be interpreted as the investment return or the yield to maturity.

To simplify it further, we can use a one-year zero coupon bond with a face value of 1 unit and divide it by the spot rate for the period from time zero to time T. This can be extended to multiple periods by discounting each period accordingly to get the discount factor, denoted as dt.

So, this is the generalized formula for the spot rate that incorporates the discount factor.

I hope that clarifies the concept of spot rate for you guys. If you have any questions, feel free to ask.