This workout. We're asked to identify the components of return over a one-year time Horizon, but the following Bond upon which has a settlement date of the 1st of January of 2050 maturity four years later in 2054. We've got a coupon of 3% for years to maturity and we're assuming that is an annual coupon. We're also told what the yields maturity is right now with four years ago at five percent. And also we're told the yield on an equivalent. three majority Bond Which is 4% Further information that were given were expecting to see a parallel yield curve shift up of one and a half percent over the course of the next year. And also a narrowing of credit spreads over that same time Horizon of 0.5% So I decrease in credit spreads of 0.5% across the whole of the yield curve over the course of the next year. Now to calculate the components of return we need to look at the coupon return and the coupon returns nice and straightforward. We just need to pick up the 3% coupon rate. That's the return would expect to make over the course of the next year from that coupon payment. The roll down return is the return would expect to make if the yield curve Remains the Same. We need a bit of a calculation here. Let's see what the price of the bond is at the moment. And then what the price of the bond would be in a year's time if the yield curve didn't change at all. We're going to assume we've got a hundred of par value. So let's start off with the current bond price. So we're going to use a negative present value function. We need our current discount rate of 5% We need a number of years to maturity. That's four. Read our coupon payments which is 3% and multiplied by the par value of 100 and then I'll par value over 100.

Which gives us the current price of the bond to be 92.9? And then we also need to calculate the price of the bond if the yield curve didn't change shape. So again a negative present value function our discount rate. Well, we're told in the scenario. That's the yield maturity on three year maturity bonds, which our bond will be in a year's time is 4% So we're going to assume that doesn't change. We've then got the number of time periods to maturity. Well at the moment we got four years to maturity about a year's time. There's going to be one less. So I'm going to take one away from that. Our coupon payment won't change it will still be the 3% of our par value of 100 and the par value also 100.

This tells us that if we do not think that yield Curve will change shape over the course of the next year. Then the price of the bond will increase from 92.9 up to 97.2 over the course of the Year giving us a rate of return from just rolling down the yield curve from yields getting smaller with our assumed upward slope to our yield curve. We're gonna get A percentage growth by taking the price expected in one year's time dividing it by the current price now and taking one away. A price increase of 4.6% if the yield curve didn't change shape. That we refer to as the roll down return. We're going to get just because We have an upward sloping yield curve. We can then overlay on top of this what we expect our changes in interest rates to be so. So to get the change in the bonds price for a change in interest rates, we need to calculate next our duration number. We're looking for modified duration because we're looking at changes in the bonds price in percentage terms. So what if I duration the M duration function we need the settlement date.

and the maturity date the coupon rate next And then are yield? We're going to assume manual cash flows. So just one here to give us our modified duration of three point six. That's a whole number what we can interpret this as a 3.6% change in the bonds price for a 1% changing you. So, let's see what the impact is of our expected change in yields. We need to take that expected change in the yield curve. a 1.5% increase in the yield curve and multiply this by negative of our duration number if there was a 1% change in interest rates, you'd expect a 3.6% change in the price of the bond, but we've got a 1.5% change in interest rate. So 50% bigger 5.5% It was an increase in interest rates that we were expecting. So it's going to be a decrease in the bond price because of the anticipated change in the shape of the yield curve. And then finally credit spreads or credit spreads are part of our yield. So the impact of this expected change in credit spreads. We just take that expected changing credit spreads of them getting narrower by half of 1% and multiply that by on negative. duration metric gives us a positive outcome to say that if credit spreads narrow that would give us a positive impact. Narrowing credit spreads are consistent with lowering yields lower yields translated to higher prices. So that will be the impact of our changing credit spreads a 1.8% positive impact on our portfolio.

Giving us overall and expected return of 4% over the course of the next year. We're getting 3% from the coupon. 4.6% return is what we'd expect to get if interest rates didn't change but interest rates are expected to increase and therefore we expect upon prices to four by five point five percent as a result of that change in interest rates. And credit spreads are going to narrow again leading to a positive impact on our portfolio. Overall, we expect a return of 4% over the course of the next year.