carry roll down

[orit]

Hi David,
Can you please clarify the topic of carry roll down:
Here we examine 3 possible assumptions made by investors?

1. If forward rates are realized it means that investing in long term bond equal rolling over shot term bonds and the investors are indifferent between the two options? is this explained by Tuckman chapter 2: maturity and bond return?
2. In respect to the unchanged term structure - can you please explain?
3. The third assumption is that the bond's yield remains unchanged
Are those assumptions realistic?
Thanks,
Orit

 

[chiyui]

I'm not sure if my answer can help you but I'll try.

For your first question, yes. If you long-term invest at the forward rates, then the return is equal to if you short-term invest at the spot short-rate and roll over.
But in reality, you won't do this. Suppose you invest $100,000 at the forward rates for 10 years. And suppose you invest the same amount of $$ at the short-rate for 1 year and roll it over for 10 years. If both choices yield the same return, which will you choose? Of course you will choose the latter. You don't want to lock your $100,000 for 10 years. If you choose the latter, at least you can determine if you'd like to roll over your investment after 1 year......to roll or not to roll. Both methods yield the same return, so why don't we just choose the latter?
Therefore, investors in the real world should not be indifferent between the two options. They also concern this liquidity issue, and they will require an extra reward on it. This means the long-term investment return should be larger than the observed forward rates.

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For your second question, I think it means like this: in your first question, there is a condition required to let both investment options yielding the same return - all the interest rates (including in the future) remain unchanged. If they change then well, you will be uncertain of the new rate when you roll over 1 year later.

Suppose the 2-year long-term rate is 4%, the 1-year short rate is 2.5%, then the forward rate is 5.52% (you can verify this).
If the new short-rate 1 year later is just 5.52%, then of course you'll earn the same return for both options.
But if it's not certain to be 5.52%, then it's another story (and a case more realistic).
If it becomes 6% 1 year later, then of course you'll be XD. You earn more by choosing the second option.
But if it becomes 5% only, you'll be orz and you'll regret not to have chosen investing long-term at 4%. (1.025*1.05 < 1.04*1.04)

In financial jargon, we will say that the term structure of interest rate does not change in order to make both investment options yielding the same return.

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For your third question, the reasoning is just the same as above. So we require the bond yield remains constant so as to make both investment options yielding the same return.
But as you can guess, this is not a realistic assumption. Bond yield does change due to a variety of reasons like a change in monetary policy, a change in bond issuer's credit quality, a change in investors' risk appetites, and so on.

So in reality, it is not easy to determine whether you should invest long-term or invest short-term with rolling-over. And that's why many people research in interest rate models like Vasicek or CIR or HJM in order to help determining whether and when you should invest long-term or short-term.