# Forward rate discounts

I'm working with the following task:

"You are convinced that the bond market is dominated by long-term investors. Hence, you have your own view on the liquidity premium/discount that forward rates embody. Given that, do you think that a duration of 3 years for this portfolio is a good idea or a duration of -3 years would be better?" (The provided yield-curve is upward sloping).

First, liquidity discount and premium are in contrast to each other?

Second, could anyone explain why/if the forward rates embody a liquidity discount because the market is dominated by long-term investors?

What does it involve if the forward rates embody a liquidity discount, and what will this imply for the future expected rates?

This is the solution, but it doesnt make much sense to me:

"Market dominated by long-term investors ⇒ Liquidity discount ⇒ E[r] > f Upward sloping yield curve ⇒ f > y0 In other words, forward rates above current yields. And, on top of that, we need to take into account the liquidity discount to obtain the expected short rates. Hence, future interest rates are expected to increase and, thus, one would prefer a portfolio with a duration of -3."

What are your assumptions about a market dominated by long term investors?

• For example if the market is dominated by investors does that mean demand outweighs supply so that yields are generally lower?
• Does long term mean this level of demand for bonds will persist for a long time or that the investors are predisposed to buy maturities of durations longer than another?
• Do your long term investors have the ability to buy short term maturities and roll them on an on going basis to allow them the possibility of investing for the long term via multiple short dated instruments?

• Is your market very large and liquid (like US or UK treasuries), i.e. you expect prices to be more transparent and have narrower bid-offer spread so that execution costs are small?
• Is your market illiquid because your investors are buy-and-hold so that there is effectively no secondary market (like SEK or NOK corporate bonds).
• what impact does each have on the supposed prices of securities.

• are you basing the answer to the question solely on this one aspect of knowledge and ignoring all other factors, such as current yield levels and view of the direction of interest rates?

I know this isn't an answer to the question but I have seen first hand how models do not reflect reality and this model seems incredibly simple for this type of analysis. I don't agree with the solution because I don't agree that the 'implications' will always be upheld, and there are 3 of them before the conclusion with scope for much argumentation. This is my own pragmatic view and not necessarily consistent with any of the academics that you are being taught so take it with a pinch of salt.

First, liquidity discount and premium are in contrast to each other?

Normally, discount and premium are opposites. For example, a bond is trading at a premium to par price if the price is over \$100, while it is at a discount if the price is below \$100.

However, it is extremely rare to see anyone use "discount" in this context, since "discount" has another important meaning in the discussion of yield curves. It is more typical to refer to a negative "term premium" or "liquidity premium." (Some economists use "liquidity premium" for what most people refer to as the "term premium.")

Second, could anyone explain why/if the forward rates embody a liquidity discount because the market is dominated by long-term investors?

As a long-term investor, this makes no sense - it implies that long-term investors are idiots. Presumably what is meant that there is a market segmentation issue, with the demand for long-dated bonds greater than the supply.

What does it involve if the forward rates embody a liquidity discount, and what will this imply for the future expected rates?

Forward rates are what are observed in the market the expected rate plus the premium (or discount, sigh...). If there is a discount, forwards are below expected (which are unaffected).

As for the solution, if forward rates are below expected, the expected return of a long position is below the expected return of cash over the period. As such, you want to be short duration.