How does selling bonds affect portfolio yield?

I’m going to give you a rule of thumb for estimating portfolio yield after rebalancing (a.k.a., liquidating) your bond investment portfolio.

If you don’t already explicitly know this rule of thumb, I am pretty certain that you have developed the intuition for it.

However, here is the value add: teach this rule to your boss, and you will make him feel very smart.

Feeling smart feels good.

Portfolio rebalancing

There are times when portfolio rebalancing triggers the question: what is going to happen to my prospective portfolio income once rebalancing takes place? It’s a very astute question because CFOs and Treasurers need to understand the impact for P&L planning purposes.

Normal turnover rate

Portfolio rebalancing turnover rate varies by investment strategy and manager style but, in general, I’ve noticed that for a short duration bond portfolio, the normal rate is about 15% per quarter (60% per year). This captures rebalancing due to duration resets that occur at the end of each month, as well as changes in sector allocations (e.g., reducing exposure to corporate bonds and adding treasuries).

Rule of thumb

Now, on to the rule of thumb.

Δ in 12-month portfolio income = ((realized gain/loss) ÷ duration) x (-1)

It is fast and simple. For example, let’s say your portfolio duration is 2.5 years and that you’re contemplating a rebalancing that will trigger $10 million in realized gains.

(a) Δ in 12-month portfolio income = ($10M ÷ 2.5) x (-1)

(b) Δ in 12-month portfolio income = -$4M

By taking $10 in gains and reinvesting in the same portfolio strategy, you should expect to decrease your interest income by $4M over the next year.

Conversely, if rebalancing resulted in realizing $10M in losses, the expected interest income would increase by $4M.

Note: One important assumption for this rule of thumb is that the funds are reinvested in a similar strategy (similar duration).

Why does the rule work?

The math behind is simple.

Let’s walk through an example.

  1. Suppose we invest $100M in a 2.5-year duration bond when interest rates are at 5%

All else equal, this investment is expected to generate interest income of $5M over the next 12 months.

  1. A moment later, interest rates decrease from 5% to 4%

With basic duration math, we can estimate the change in market value of our bond.

(a) Δ in bond market value = Δ in interest rates x duration x (-1)

(b)Δ in bond market value = (-1%) x (2.5) x (-1)

(c) Δ in bond market value = +2.5% → or $2.5M

  1. Our bond is sitting in an unrealized gain of $2.5M
  2. We sell our bond and realize the $2.5M gain
  3. We reinvest in a similar bond

Investment amount = $102.5MCurrent interest rate = 4%Expected interest income of new bond: $102.5M x 4% = $4.1M

  1. So, our expected income has decreased by approximately $1M from $5M to $4.1M
  2. Our rule of thumb would have given the following answer:

(a) Δ in 12-month portfolio income = ((realized gain/loss) / duration) x (-1)

(b) Δ in 12-month portfolio income = (($2.5M) / 2.5 years) x (-1)

(c) Δ in 12-month portfolio income = -$1M

… pretty close, huh?