# CFAI Reading 28 Example 8

I do not understand solution 2 on immunized target rate of return , any explanation will be greatly appreciated. TIA

If the term structure is upward sloping it means that long term maturity rates are higher than short term rates;reinvestment of cash is done on the short-end of the term structure. Hence, reinvestment returns are being invested at lower rates dragging down the target rate vis a vis the YTM. (Why the YTM is higher is for compensation from holding long term bonds and all that level 1 fun stuff). The opposite is true for the inverse scenario.

Thanks for sharing. Why “reinvestment of cash is done on the short-end of the term structure”?

You are reinvesting coupons for no longer than six months…

Why the reinvesting coupon needs to be less than 6 months? What if the liability is 20 years away? TIA!

This is NOT cash flow matching! The liability is immunize with the market value of assets not the cash flows. The reinvestment is part of the immunization of the portfolio in order to offset market value fluctuations with changes in interest rates. Extension risk will occur if you invest coupons for the long term…better to invest in the overnight spot market and t-bills and rollover proceeds to capture the interest rate levels that affect the assets.

The target rate of return is the assured rate of return at the beginning of the investment and assumes no change in the term structure. This target return is based on the Yield curve a the point of investment. Naturally, the Yield curve will keep changing, but then the target return then stays the same unless the yield curve is flat. So lets assume your beginning horizon is at point Y in time. If the curve is upward sloping, then your target return is lower than the YTM because the portfolio will be immunized at lower investment rates. If the curve is downward sloping, then the portfolio target return is higher than the YTM because it is immunized at higher reinvestment rates. Hope that help.s

I’m confused about the problem # 9. Where is the formula applied here? I’m totally lost here.

derswap07, what is problem #9?? I was asking example 8, which is quite confusing.

I have the same issue with problem 9. Explanation will be appreciated.

So just to put this in perspective.

for the portfolio manager an upward sloping yield curve is good because he will surpass the target value?

Q 9

“5-year: T 4.125% 15May2011”, 4.53 , 100.40625

10-year: T 5.25% 15May2016 8.22, 109.09375

Question asks for "“the par value of 10-year bonds to be purchased to execute Alonso’s strategy is closest to:” What Alonso wants to do: ““Alonso has done further analysis of the current U.S. Treasury portion of the portfo- lio and has discovered a significant overweight in a 5-year Treasury bond (\$10 million par value). He expects the yield curve to flatten and forecasts a six-month horizon price of the 5-year Treasury bond to be \$99.50.” Alonso’s strategy will be to sell all the 5-year Treasury bonds, and invest the proceeds in 10-year Treasury bonds and cash while maintaining the dollar duration of the portfolio.”

Dollar Duration of Bonds Sold = 10 M in Par * 100.40625 /100 (Price) * 4.53 * 0.01 = 0.4548403 M

Now he buys say X Mill \$ in Par of the 10 Year Bond.

Dollar Duration of That = X * 109.09375 / 100 * 8.22 * 0.01 = X * 0.089675

Both the above are equal. Solve for X

0.4548403 / 0.089675 = 5.072097 M

Ans A.

Thanks CPK123 but I was actually just asking

For the portfolio manager an upward sloping yield curve is good because the YTM will be higher then then target immunized value?

There for he will be able to easily fund the liability that is being immunized with some extra return on top?

is that correct?

The YTM implicitly assumes that you will reinvest any and all coupons at the YTM as they are earned.