(a) The S&P/ASX200 price index moved from 6,120 to 6,600 in a year. The S&P/ASX Small Ordinaries index went from 2,800 to 2,700 over the same period. What is the effective annual rate of return on each of these indices? Explain the difference in information provided by these two indices.

(b) Using the approach covered in your textbook calculate the annual forward rates of return out to five years given the following annual spot rates, one year (0z1 = 0.78%pa), two year (0z2 = 0.84%pa), three year (0z3 = 0.91%pa), four year (0z4 = 0.99%pa), five year (0z5 = 1.10%pa). What does this imply about future interest rates? TIP: you might find equations 3.13 and 4.11 to be useful starting points.

(Rates as a percentages accurate to one basis point)

Can you show me the excel formula you have used and the workings?

on the day 2 years from ent per annum over the CHAPTER FOUR APPLYING THE TIME VALUE OF MONEY TO SECURITY VALUATION Similarly, today's 3-year interest rate, Zo,3, is determined from today's 1-year interest rate, the 1-year interest rate in a year's time and the 1-year interest rate in the year after that. That is, structure. ( 1 + zo, 3) = (1 + zo, 1) (1 + 21, 2) ( 1 + Z2, 3) rate is 6.5 per cent per Generalising, for any given term of t years, today's t-year interest rate Zo, is set by the market such that: 21 per cent per annum, ( 1 + zo, t ) = ( 1 + zo, 1 ) ( 1 + z1, 2) (1 + zz,3) ... ( 1 + 2+-1, t ) hat the same return is Rearranging this equation, today's t-year interest rate zo, is given by: zo,t = [(1 + zo,1 ) x (1 + z1, 2) X (1 + Z2,3) X . .. x (1 + zt-1,t)]/t - 1 4.11 Thus, in our earlier discussion, using Equation 4.11 gives the 2-year interest rate as: ZO,2 = (1.065 x 1.095 21) 1/2 - 1 = 8% per annum and the 3-year interest rate is: Z0,3 = (1.065 x 1.095 21 x 1.11028) 1/3 - 1 = 9% per annum 3 years The essence of expectations theory is that the term structure is determined by investors' expectations of short-term rates within the maturity of the competing long-term security." Expectations theory can help to reconcile the existence of the differing shapes of the term structures shown in Figure 4.1 and the yield curves shown in Figure 4.2. In general, an upward-sloping term structure implies that investors expect future short-term interest rates to increase. 10 In that case, investors are not prepared to invest in long-term securities unless the eater than that on short-term securities, because otherwise the investors would be better off cities and reinvesting the proceeds at maturity. ure implies that investors expect future short-term se long-term securities yielding less ed an investment LiQImight follow the normal normally distributed. A generalisation: geometric rates of return geometric rates of return, the rate, into Pound interest is a special case of a geometric rate of return Themetric compound inter RATE OF RETURN interest rate is the same in each period. In the more general case of geor the can be different in each period, While the sum invested is still subject to the compounding rated quence rates of the rate at which compounding occurs will differ from period to period. d by a Pose that $1000 is invested for 4 years and each year the investment earns a different . embles unding return, as follows: . In Year 1: 10 per cent per annum . In Year 2: 5 per cent per annum . In Year 3: 8 per cent per annum In Year 4: 15 per cent per annum. The value of this investment therefore grows as follows: 1 At the end of Year 1: $1000.00 x 1.10 = $1100.00 At the end of Year 2: $1100.00 x 1.05 = $1155.00 3 At the end of Year 3: $1155.00 x 1.08 = $1247.40 4 At the end of Year 4: $1247.40 x 1.15 = $1434.51. Of course, this result could have been found more quickly and conveniently by calculating, in one ster $1000 x 1.10 x 1.05 x 1.08 x 1.15 = $1434.51 Writing the calculation in this way emphasises the similarity between compound interest and the more general case of geometric rates of return. It is natural to ask: what annual compound interest rate would have produced the came result? In other words, what single rate of return i per year would need to be earned in each of the 4 wars, to produce the same future sum? To answer this question we need to solve: $1000 x 1.10 x 1.05 x 1.08 x 1.15 = $1000(1 + i)4 that is, i = [(1.10) (1.05) (1.08)(1.15)]1/4 -1 = (1.434 51) 1/4 -1 =9.440% per annum In fact, i in this calculation is the mean (or average) geometric rate of return. It is the rate of retum which, if earned in every period, and allowing for the effects of compounding, would produce the same outcome as that actually observed. In the general case, the mean geometric rate of return is: i = [(1 + r,) (1 + 12) ... (1+ In)]1 - 1 where rx = the rate of return in period k 3.13 k = 1, 2 , ..., n n = the number of completed periods