[MUSIC] In the previous part of this segment, we've seen that interest rate for lending that covers a period spanning a monetary policy meeting will reflect a combination of policy rates before the meeting and market sentiment about the likely policy rate following the meeting. In this part of the segment, we show the implication for slightly longer term lending. Forward rates are useful for thinking about the relationship between interest rates with different maturities. Consider if you look at the market today. You observe two interest rates. One for loans to be repaid in K days, this is called i subscript K. Another is the interest rate on loans to be paid in N days, called i subscript N. N is farther in the future than K. We call these interest rates spot rates because they are interest rates for loans made on the spot, meaning right away. Consider the Thai Baht money market during the period of policy tightening in 2011. On June 22nd, the policy interest rate has reached 3%. The interest rate on one month inter bank loans to be repaid on July 22nd is 3.075%. And the interest rate on 2-month loans to be repaid on August 22nd is 3.164%. In this case, a 1-month loan is for 30 days, since June has 30 days, and a 2-month loan is 61 days, as July has 31. The longer term interest rate can be decomposed into two parts. The short term interest rate plus the forward rate, a hypothetical interest rate of the future. We can think of the forward rate as a contracted interest rate on a loan that is lent out with a delay of K days for repayment on day N. So the hypothetical loan lasts for N- K days. We call the forward rate here f subscript + K, N- K. Note that we will think of the forward rate as a theoretical construct, though in some markets, derivative traders may offer delayed loans at a forward rate. The forward rate can be thought of as that part of the interest which is payment for the time after day K for N- K days through day N. To calculate the forward rate, think of the interest rate over N days as the sum of the shorter term interest rate and the forward date. Specifically, i subscript N is a weighted average of the short term interest rate iK and the forward rate. With the weights being a fraction of the N days that the spot and forward rate apply respectively. The short term rate is operative for K out of N days, and the forward rate is operative for quantity N- K out of N days. With this definition, a little algebra will allow us to calculate the forward rate. Multiply both sides of the equation by N. Subtract K times iK from both sides of the equation. Divide both sides by N- K to solve for the forward rate. The forward rate can be thought of as that part of the interest which is payment for the time after day K for N- K days through day N. Calculate the forward rate in the Thai Baht money market on June 22nd, 2011. We can calculate the forward rate using the formula with K = 30 and N = 61, and N- K is 31. The forward interest rate for a loan to be disbursed on July 22nd and subsequently repaid August 22nd could be calculated using the June 22 one month rate and the two month rate. The one month interest rate is 3.075%, and the two month interest rate is 3.164%. We can calculate the forward interest rate is almost exactly 3.25%. This is higher than the spot one month interest rate. Why is the interest rate on the second half of the two month interest rate higher than the interest rate on the first half? The expectations theory of the term structure is used to explain the forward rate. In this theory, forward rates represent the market's expectation of the spot interest rate over the time period covered by the forward. Continue the example of the comparison between the one month interest rate and the two month interest rate. The implied forward rate would cover a hypothetical loan to be lent from one month from now and repaid two months from now. Market observers form expectations of what the short term interest rate will be one month from now. According to the expectations theory, the forward rate should reflect market expectations of the interest rate prevailing over future periods. To see the implications for monetary policy, return to the Thai interbank market on June 22nd, 2011. We calculated the implied forward rate on that day at 3.25%. Why should that be? On June 22nd, policy rates were set at 3%. But a lender would also know that the Monetary Policy Committee was scheduled to meet on July 13th. As they have continuously raised interest rates by 0.25% for the past half dozen meetings, it is reasonable to expect that they will be likely to raise interest rates again to 3.25% at that next meeting. This would mean the interest rate would be 3.25% on July 22nd and the entirety of the following month, as the Monetary Policy Committee would not be scheduled to meet again until August 24th. Thus, it is reasonable to assume the interbank rate will be 3.25% over the period July 22nd to August 22nd. It makes sense to price a forward rate of 3.25% into a two month loan made on June 22nd. This is exactly the forward rate we see on the two month interest rate. Thus, the forward rate is a reasonable expectation of the interbank rate over the relevant future one month period as the expectations theory predicts. Notice that interest rates increase in anticipation of each meeting. On June 22nd overnight interest rate is 3%. The lenders would not want to lock in their money for one month at 3%, since toward the end of the month, interest rates will increase by 0.25%. So lenders will only lend in the one month market if they get a little bit more than 3%. But the closer that lending gets to the meeting day, the more incentive lenders have to hold onto their money until rates go up. On the day before the meeting, the rates on one month lending have already increased almost to 3.25%, even before the central bank has acted. Longer term loans are less liquid than short term loans. In the case of unexpected changes in plans, it is easier for a bank to change its lending patterns when the short term loan is repaid. Banks charge somewhat higher rates for longer term loans. For instance, an interest rate for X months would be the average of the short term monthly interest rates over the X month plus some additional liquidity premium. For example, when we examine the Bangkok interbank market, the longer term interest rates follow the monetary policy rate as in expectations theory. However, we also see that longer term interest rates are consistently slightly higher than short term rates, though the expectation theory is useful for thinking about the trajectory of monetary policy. The interbank rate will be guided by expectations of future monetary policy. But this rate should in turn guide interest rates in the broader money market. The interest rates on three month government securities closely follows the BIBOR rate. If interbank interest rates were lower than securities yields, the banks could borrow in the interbank market and buy government bills. This would bring the rates in the bill market down. If the interest rates in the government securities market were low relative to the BIBOR rate, then banks would sell government securities, which would increase the rates in the treasury bill market. We also see that the rates on retail time deposits and the prime rate for retail bank loans also somewhat follow how much it costs to borrow in the interbank market. After completing this segment you should be able to, 1, calculate the effect of policy rates on longer term money market rates. Now let's conclude by summarizing the key question. What is the impact of monitory policy rates on the money market? Money market rates reflect not only today's policy rates, but also the expected monitory policy decisions over the next year. Lenders and money markets will choose between lending long term and rolling over short term loans. Markets should roughly equalize the expected returns on the two strategies. In this case forward rate should equal the market's expectations of future short term rates. Thus, market expectations of future monetary policy rates should be reflected in longer term interest rates. Well, we've covered a lot of material. Let's wrap things up by turning to a summary video.