Dear David,

You write a lot about rebalancing your portfolio. How do you measure how far out of balance a portfolio is? What is too little to matter? What is too much and I should take action?

Sleepless in Charlottesville

I created a number which we use in our firm as a measure of how far out of balance a portfolio is from its target values. We call this measurement “**the out of balance**” measurement or the “**account delta**” number or the “**asset allocation deviation**“.

First we use group accounts in our systems to aggregate several actual accounts into a single portfolio view for asset allocation and reporting purposes. Each client household has a group account which represents their primary retirement account and we record a target asset allocation for this account. This allows us to view all their assets together for portfolio asset allocation and rebalancing, and still put different asset classes in different investment vehicles. Then we track and record how far from a perfect asset allocation each client’s primary retirement account is each week.

The formula for this out out of balance measurement is based on a number of ideas:

- First, that it isn’t necessary to measure any out of balance which is less than about $1,000. When you are just getting started, I recommend you buy something for at least a few thousand dollars and then buy the next time with the next chunk of money. It isn’t important to have a balanced portfolio for small numbers.
- Second, it becomes more important to rebalance categories which are a greater amount out of balance. Each asset class should be within 5% of your targets.
- Third, the number must aggregate the out of balance measurements across each asset categories and provide a single number with values which represent “good enough” and “nearly perfect”.

Here is the out of balance number is computed and how those criteria are used:

For each asset allocation category:

CategoryDeviation = pow(log((abs(TargetPercent – ActualPercent) / ThresholdPercent) *

e+ 1), 2) * log(max(abs(TargetCash – ActualCash) / ThresholdCash,1));Where ThresholdPercent = 5; and ThresholdCash = 1000; and log is the natural log (ln).

Or to simplify the idea

CategoryDeviation =

PercentFactor * CashFactor;Where

PercentFactorgrows significant when the percent is off more than 5%and

CashFactorgrows gradually based on the natural log of how many thousand of dollars the category is off.

Finally we add up all the CategoryDeviations to get a total out of balance measurement.

Here is a sample asset allocation for a $5M account along with, for each asset class: DeltaPercent = abs(TargetPercent – ActualPercent); and the CategoryDeviation (PercentFactor * Cash Factor)

9.68%Short Money (Target=3.00%) DeltaPercent =6.68%CategoryDeviation =13.66(2.35 * 5.81)

8.24%US Bonds (Target=9.70%) DeltaPercent =1.46%CategoryDeviation =1.47(0.34 * 4.29)

8.20%Foreign Bonds (Target=9.70%) DeltaPercent =1.50%CategoryDeviation =1.54(0.36 * 4.32)

23.68%US Stocks (Target=25.50%) DeltaPercent =1.82%CategoryDeviation =2.14(0.47 * 4.51)

33.50%Foreign Stocks (Target=35.10%) DeltaPercent =1.60%CategoryDeviation =1.71(0.39 * 4.38)

16.70%Hard Asset Stocks (Target=17.00%) DeltaPercent =0.30%CategoryDeviation =0.06(0.02 * 2.71)TOTAL Portfolio deviation score:

20.58(the total of all six asset class CategoryDeviations)

In this case you can see that the large Short Money position is responsible for the portfolio being out of balance, but with everything else close to tolerances it is close to its targets.

We use the following scale for our of balance measures:

<5: Nearly perfect

5 – 25: Close to tolerances

>25: Out of balance

We use these measurements to generate automatic alerts for portfolio review in addition to the normal calendar reviews.

Here is another sample portfolio for a $2M account:

10.00%Short Money (Target=3.00%) DeltaPercent =7.0%CategoryDeviation =10.47(2.46 * 4.25)

30.00%US Bonds (Target=9.70%) DeltaPercent =20.30%CategoryDeviation =32.89(6.19 * 5.31)

0.00%Foreign Bonds (Target=9.70%) DeltaPercent =9.70%CategoryDeviation =15.43(3.37 * 4.57)

60.00%US Stocks (Target=25.50%) DeltaPercent =34.50%CategoryDeviation =52.01(8.90 * 5.84)

0.00%Foreign Stocks (Target=35.10%) DeltaPercent =35.10%CategoryDeviation =52.74(9.00 * 5.86)

0.00%Hard Asset Stocks (Target=17.00%) DeltaPercent =17.00%CategoryDeviation =27.80(5.41 * 5.14)TOTAL Portfolio deviation score:

191.34(the total of all six asset class CategoryDeviations)

This is a typical asset allocation for investors who don’t invest in all six asset categories. Although the same targets are in place as the first example. This portfolio is out of balance in every category with an out of balance score of **191.34**.

We use this measurement to communicate to new clients how close we are toward adjusting their portfolio to the targets we have set. If the initial portfolio is out of balance **100.00** and we have reduced that number to **30.00** we could say that we are 70% of the way to being perfectly in balance.

Our method of measuring how far a portfolio is out of balance may seem a little technical. But then we love math, and the formula even uses my favorite number *e* (2.7182818…).

The important point is to rebalance regularly between asset classes and subcategories. Portfolio rebalancing boosts returns.

## 2 Responses

## Dave Kretzmann

I very much appreciate all your articles and answers to reader questions. This one was particularly interesting, so I constructed an Excel spreadsheet to try to replicate your example portfolio results (before adapting to my own allocation categories and targets).

I noticed a small error in your second example. The Cash Factors and Total Deviation come out right only if the portfolio account size is $1M (vice $2M).

## Mert

Wonderful article! I immediately applied the knowledge to my portfolio in excel.

Thank you very much.