Making my way through the material, I’m realizing I’m shaky on some of the basics. I’m not sure if I made it here somehow without learning them in the first place, or have forgotten, since it’s been so long since level 1 and 2(8 years since L2)
Anyway, I was hoping someone could provide me some insight on some questions I have on some fixed income basics.
It’s always assumed that cash flows are reinvested at the discount rate? Why is this a necessary assumption? How would things be different if this weren’t the case?
Macauley Duration is explained to be the balance point where price and reinvestment risk offset each other. Why is that so?
Say you have 3 investors.All 3 invest in the same issue. Let’s say the cpn is 7%. And market interest rate is 6%…which also is the discount rate. All other things remaining constant the theoretical price of this issue will be above par for a 5 year period.
Now let’s say the 01st Investor intends to hold onto it till maturity
The 02nd Investor has an opportunity to re invest the periodic cpn at 10%
The 03rd Investor has an opportunity to re invest the periodic cpn at 12%
So what is the theoretical price of this bond ?
Surely 3 different prices can’t exist without invoking arbitrage profit .
Since the market can’t figure out every individual’s re investment options the safest assumption is the periodic cpn are re invested at the yield only .
Yup. CFAI has funny ways to twist and turn an otherwise simple concept. Especially with FI hey are leaving no stone unturned to muddle underlying principles.
A Macaulay duration is ONLY appropriate for a zero cpn bond … and for the investor who Wanstead to hold on to it full maturity. Unless defaulted… the yield is exactly known beforehand. Such an arrangement will render the investor risk less. Which again is the exact point of intersection of the Price risk and Re investment risk. That is no risk. Now for any such intersection point a zero cpn must exist.
Your quest starts with pricing the bond. That is how you would arrive at the theoretical price. You are right. It should not matter how cpns are re invested.
For if it did matter then everybody’s price for the same issue will be different. How would one arrive at the theoretical price then ?
Hence the safest assumption is should you receive the periodic cash flows then those cash flows must be re invested at the same discount rate for the remainder of the tenor. That is how the YTM is arrived at as well.
There are two schools of thought on IRR (which is what YTM is):
Because IRR is simply a discount rate to get the present value of future cash flows, how future cash inflows are reinvested (and, specifically, at what rate) has no bearing on IRR calculation. Put another way, once cash flows are received, they’re no longer considered part of this investment.
Because IRR is a rate of return (which relates the future value of the investment to its present value), all cash flows are considered part of this investment until the end of the holding period. Therefore, the reinvestment income on cash inflows is considered to be part of the future value, so the reinvestment rate will affect the IRR.
There are advocates for each of these schools of thought.
By thinking of the IRR as simply a discount rate, as in your first bullet point, isn’t there an implicit assumption that the cash flows are compounded (reinvested)?
For example, if a two-year bond is trading at par, with a 5% YTM, CF1 = $5 and CF2 = $105. If we assume no reinvestment, at the end of year two we’d have $110. ($110/$100)^1/2 - 1 = 4.88%. But if we discounted the cash flows using 4.88%, we’d get a PV of $100.22 rather than $100.
I know that’s not discounting. What I don’t understand is how one group can assume cash flows are reinvested, while the other assumes they’re not reinvested, yet they both use the same IRR to equate the future cash flows to the bond price. That seems mathematically impossible.
It’s possible that I’m just not understanding your post correctly. For the record, I have always thought of the IRR in the way described in your second bullet point.
Suppose that you buy an annuity, and you use the payments for living expenses. You’re not reinvesting the cash flows, but you calculate the price the same way you would if you’d bought a bond, and the discount rate is the IRR.
