The return a mix can expect
A portfolio's expected return is the average of its parts, weighted by the money in each. Fees come straight off the top.
- Blend three sleeves into one expected return
- Take the fee off in dollars and in percent
- Find the equity weight a plan's target return needs
- Say why volatility does not blend the way return does
The intuition
A client has $1,000,000. Sixty percent sits in equities that should earn about 7% a year, thirty-five percent in bonds that should earn 4%, five percent in cash at 2%. Nobody needs a model to guess the portfolio's expected return: it is somewhere between 4% and 7%, closer to 7% because more of the money is there. The exact answer is the weighted average, 5.7%, and it is the one portfolio number that is genuinely easy.
That easy number is why the allocation decides most of what happens to a client. Moving ten points from bonds to equities adds ten percent of the gap between them, every year, for as long as the mix is held. The fee comes off the top of the blend, so it is small against the portfolio and large against the return. Run the blend backwards and it answers the question clients actually ask: how much equity do I need to hit the return my plan assumes?
Expected return = equity weight × equity return + bond weight × bond return + cash weight × cash return. Net of fees = that − fee. Equity weight for a target, cash fixed and bonds taking the rest = (target − cash weight × cash return − (1 − cash weight) × bond return) ÷ (equity return − bond return).
Why it works
- The conventions here: three sleeves with one-year expected returns, before fees; the weights sum to one. The advisor's fee is a flat share of the starting value, charged once for the year.
- Return is linear in the weights. Each dollar earns its sleeve's expected return, so the portfolio earns the money-weighted average. No correlation, no diversification: those belong to risk, not return.
- Equities carry the return. In a balanced portfolio most of the expected return comes from the equity sleeve, and an even larger share of the risk. "60/40" describes the capital, not where the return or the risk sits.
- The fee is charged on the whole portfolio, not on the gain. One percent of $1,000,000 is $10,000, which is a sixth of a $57,000 expected gain. Clients live on the return, so the fee's honest size is its share of the return.
- Run it backwards for the plan. A plan that assumes 6% needs a certain equity weight given what equities and bonds are expected to earn. If the client holds less, the choices are more risk, a lower assumed return or more saving; hoping is not one of them.
- Risk does not blend. Volatility is at or below the weighted average of the sleeves' volatilities, equal only when they move in lockstep. That is the next chapter, and the one free lunch in allocation.
| Blended return: 60% × 7% + 35% × 4% + 5% × 2% | 5.70% |
| Expected gain: $1,000,000 × 5.70% | $57,000 |
| Fee: $1,000,000 × 1% | $10,000, so $47,000 net (4.70%) |
| Equity for the 6% target, cash fixed: (6% − 0.1% − 95% × 4%) ÷ (7% − 4%) | 70% |
| Ten points from bonds to equities: 10% × (7% − 4%) | +0.30%, or $3,000 a year |
The fee is 1% of the money and 17.5% of the expected gain. Both statements are true; the second is the one that matters to the client.
The formulas
Each sleeve's return, weighted by its share of the money.
The fee comes straight off the blend.
The blend in dollars.
The blend run backwards, with cash held and bonds taking the rest.
Only the moved slice changes.
Worked example
Blend the three sleeves, apply the blend to the portfolio for the gross gain, then take the fee off in dollars. The last line is the same in percent.
See it move
Same client and the same expected returns. Change the equity weight (bonds take the rest, cash stays where it is), the advisor's fee and the size of the portfolio.
- Raise the equity weight. The expected return rises, because equities are expected to beat bonds on every draw; the fee in dollars does not move.
- Raise the fee. The net gain and the net return fall; the blended return does not move, because the fee comes off after the blend.
- Change the size of the portfolio. Every percentage stays where it is and every dollar figure scales with it.
- Slide the equity weight until the curve crosses the plan's target. That weight is the readout under the curve: the blend run backwards.
Run it backwards
The plan assumes a return; equities and bonds have expected returns; cash is fixed. What equity weight gets there?
Start from the return the portfolio would earn if everything outside cash were bonds. The gap from that to the target has to be closed by equities, and each unit of equity swapped in for bonds adds the equity-bond gap. Divide the two gaps.
The follow-up is the advisor's conversation: if the client holds less equity than the plan needs, something in the plan has to give, and it should be said out loud.
Traps
Say it in the interview
“What return should this client's portfolio expect, and what does the fee do to it?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Expected return = weights × returns, added up.
- Net = blend − fee; judge the fee against the gain, not the portfolio.
- Equity weight for a target = gap to the target ÷ equity-bond gap.
- Return blends linearly; volatility does not.