BKM ¶15 -- Liquidity Premium Question

[Avi]

I'm having conceptual difficulty with the contrasting views of liquidity premium for long- and short-term investors.

The way I understand it, is that short-term investors prefer the freedom of the short-term rollover. Therefore, in order for them to be sufficently induced to lock their money up longer term, they need to be certain that the returns in the second (or future) periods exceed what we believe they will be now. In that case, the locking is worth the risk. In BKM language, this is \small f_2 > \textrm{E}(r_2), or the required rate in period 2 to make the short- and long-term strategies equal, \small f_2 is LARGER than the currently expected future short (forward interest) rate in that period \small E(r_2).

In contrast, long-term investors prefer the knowledge of certain returns, and are worried about falling interest rates after the first period. This will lower the expected return in the second period by causing the price of a bond with the same 1-yr YTM to have a higher price, or having a bond with the same price in the second period have lower coupon rates as the interest rate has dropped. According to BKM, this requires that the expected returns on the 2-yr ROLLOVER strategy have to be greater than the 2-yr locking strategy. As \small f_2 is the rate that makes the two strategies equal, and the current short rate is unchangeable, the expected future short rate needs to be HIGHER than the current forward rate for the 2-yr rollover strategy to exceed the 2-yr lock strategy.

It is the long-term issue I am having some trouble with. Is the following a valid alternate explanation?

Long-term investors prefer the knowledge of certain returns, and are worried about falling interest rates after the first period. This will lower the expected return in the second period by causing the price of a bond with the same 1-yr YTM to have a higher price, or having a bond with the same price in the second period have lower coupon rates as the interest rate has dropped. Therefore, they have to ensure that the price of the 1-yr bond in the second period that they plan on purchasing (with the same coupon rate) is LOWER than the "indifferece" price (based on \small f_2 ); leading to a greater YTM than the "fair-priced" version. This will compensate them for the risk of NOT locking-in a good rate now. In order for the future bond price to be lower, the actual expected future rate has to be greater than the indifference rate, or \small f_2 < \textrm{E}(r_2).

:wall:

[Me3]

How's this:

Think of short-term investors as people who only want to invest their money for a short time (let's say 1 year) (Forget about rollovers -- maybe they want to buy a house in a year with the money -- whatever.) They therefore only care about today's 1 year rates and they don't care what the 1-year rates will be in one year. Their ideal investment would be one that matures in one year with a locked-in fair interest rate.

Now assume that you come along with an investment that will lock in a fair rate for 2 years (i.e., a rate based on 2-year investors’ demand). The 1-year investors would not be interested -- because if they would invest in it, they would HAVE to sell it in one year in order to get the money they need for buying that house. But the amount they will be able to sell this investment for in 1 year will depend on the 1-year yield one year from now. So now even THEY have to worry about 1-year rates in a one year.

Therefore, you would have to lower the price of the 2-year investment (from its otherwise "fair" price) so that even if the 1-year rates in one year have gone up somewhat, there is a decent chance that the short term investors will be able to sell the 2-year investment for at least the amount they need to buy the house.

Hence, if there would ONLY be 1-year investors in the market, sellers of 2-year investments would have to offer higher returns (i.e., lower prices) in order to lure these ST investors to their investments.

Equivalently, mathematically, if (1 + y2)^2 = (1 + y1) * (1 + f2) then f2 would necessarily be greater than the fair implicit rate for the second year, i.e., E(r2)


Now, think of long term investors who won't need their money for 2 years (e.g., they are making a Bar Mitzvah then). They DO NOT really care about today's 1-year rates -- nor would they care what the 1 yr rates will be in one year. Their ideal investment would be one that matures in two year with a locked-in fair interest rate.

Now assume that you come along with an investment that will lock in a fair rate for 1 year (i.e., a rate based on 1-year investors' demand). The 2-year investors would not be interested -- because if they would invest in it, they would HAVE to rollover the money into another 1-year investment in one year. But the rate they would get in one year would depend on the 1-year yield one year from now. So now even THEY have to worry about 1-year rates in one year, as they might be lower.

Therefore, you would have to lower the price of the 1-year investment (from its otherwise "fair" price) so that even if the 1-year rates in one year have gone down somewhat, there is a decent chance that the long term investors will still be able to have the money they need for the Bar Mitzvah one year later even if the rolled-over money will have earned less money.

Hence, if there would ONLY be 2-year investors in the market, sellers of 1-year investments would have to offer higher returns (i.e., lower prices) in order to lure these LT investors to their investments. This would mean that current market rates for 1-year investments would be higher than the "fair" rates would be.


Now, assume that the "fair" 2-year rate is made up of the "fair" 1-year rate and a "fair" forward rate. We could then use the formula (1 + y2)^2 = (1 + y1) * (1 + f2) to back into the "fair" f2 which = E(r2). However if there were only LT investors, we pointed out that the 1-year rates would be higher than the "fair" 1-year rates, so if we back them out of the formula (treating them as if the WERE the "fair" rates) the resulting forward rate, f2, would be LOWER than the "fair" forward rate (E(r2)).


So it comes out that long-term investors put upward pressure on the current 1-year rate, and short-term investors put upward pressure on the 2-year rate. So if we would treat the 1-year rate as "fair" (which is what we are doing) the implicit forward rates would either be higher than the "fair" forward rate (if there were more ST investors) or lower than the "fair" forward rate (if there were more LT investors).


Does this clarify things at all?

[Avi]

Yes, I think so.

If I understand corrrectly, the key point you are making is that LT investors need lower prices/higher returns now (in lieu of purchasing a long-term contract), so to keep the 2-yr SPOT rate the same (indifferent) the second year FORWARD rate drops to balance the increase in the "acceptable" current 1-yr short rate that drops the price/increases the return on the 1yr. So \small f_2 < E(r_2) .

However, short-term investors need higher returns NEXT year if they buy longer bonds, so the FORWARD rate (earned on later period of bond) needs to be higher than the current expected rate, or \small f_2 > E(r_2) .

Is that correct?

Thank you very much.

[Me3]

I would like to say yes, but I don't see the ST investors demanding ANYTHING related to next year's rates. I see them demanding higher 2-year spot rates TODAY for no reason other than as "insurance" against having to sell the 2-year investments in one year for less money than they would have gotten by investing in 1-year investments.

It is WE who are trying to interpret the market rates to decide what fair-minded LT investors are expecting next year's 1-year rates to be. (We would like to assume that LT investors demand "fair" 2-year returns -- fair in that it is what they would have expected to earn from two consecutive fairly-priced 1-year invetments (if they could guarantee the two consecutive rates.))

It is WE who therefore have to adjust our thinking about what is implied by the term structure about the expectation about next year's 1-year rate (by "fair" LT investors, who are the only ones thinking about next year's 1-year rate.) . If ST invertors behave as we describe, and they are the majority of the market, the implied (i.e., calculated) forward rate will be higher than what fair-minded LT investors would have demanded for that rate.


Maybe it is me who is looking at this wrongly, but I see the whole situation simply as one in which we have to adjust our interpretation of the market expectations based on possible "data problems" relating to the fact that the data we are using have different meaning than we are assuming in our "innocence", i.e., that (1 + y2)^2 = (1 + y1) * (1 + f2) is the same as (1 + y2)^2 = (1 + E(r1)) * (1 + E(r2)) or even that (1 + y1) is the same as (1 + E(r1)).

Does anyone else have any comments?

[mister nacho]

All that is well and good, but I think if we are asked for the reason why there is a liquidity premium on the exam, and you don't want to spend a half hour explaining it, the key words are "investment horizon."

It is assumed that investors will prefer to invest in bonds that match their investment horizon. It is believed that short-term investors dominate the market. Thus, it appears that they prefer liquidity.

Regardless of the anticipated forward rates, the reason a liquidity premium exists is because short-term investors require additional return in order to entice them to invest in longer term bonds.

Key words are important on the exam.

[volleyball]

I tend to agree, the above posts show quite an indepth understanding of how this all works, far more indepth than I understand, however the simplicity of the last post really boils down the true meaning of all this and is as much as the exam will (should) expect....I would think(hope)
:tup:

[frank_exams]

As far a Liquidity Preference is concerned, Me3 has it down.

There are two views here that need to be separated; this thought was triggered by the "innocent" equation Me3 posted.

1. Liquidity Preference Hypothesis.
Investors invest based solely upon liquidity preference. To quote Me3:

"I would like to say yes, but I don't see the ST investors demanding ANYTHING related to next year's rates."

This is true for both LT and ST under this hypothesis. Advocates of this theory believe ST investors dominate, so LT rates have to be higher to induce LT investment. Expected rates figure in, but only to the extent that the liquidity premium is predictable. (For all we know, the liquidity premium could be even a stochastic process.) However, proponents of this theory would attribute any difference between (1+y_2)^2/(1+y_1) and E(r_2) to liquidity premium.

2. Expectation Hypothesis.
Investors take into account only expected rates and expected return and completely ignore liquidity. Liquidity premium is 0 and LT rates signal only the sentiment about where rates are expected to head, e.g. if LT rates > ST rates, then you expect rates to rise (measured by the higher forward rate necessary to "catch up" to the higher LT rate). In other words, the "innocent" equation

(1 + y2)^2 = (1 + E(r1)) * (1 + E(r2))

always holds. If, for some reason, the two sides are inconsistent, this theory would explain it via differing expectations in future rates.

Frank