Simple Dietz method

Key takeaways

Simple Dietz method belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Simple Dietz method to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Simple Dietz method from memory before moving on to harder problems.

Reference excerpt

The simple Dietz method is a means of measuring historical investment portfolio performance, compensating for external flows into/out of the portfolio during the period. The formula for the simple Dietz return is as follows:

R = B − A − C A + C / 2 {\displaystyle R={\frac {B-A-C}{A+C/2}}}

where

R {\displaystyle R} is the portfolio rate of return,

A {\displaystyle A} is the beginning market value,

B {\displaystyle B} is the ending market value, and

C {\displaystyle C} is the net external inflow during the period (flows out of the portfolio are negative and flows into the portfolio are positive). It is based on the assumption that all external flows occur at the half-way point in time within the evaluation period (or are spread evenly across the period, and so the flows occur on average at the middle of the period).

Fees To measure returns net of fees, allow the value of the portfolio to be reduced by the amount of the fees. To calculate returns gross of fees, compensate for them by treating them as an external flow, and exclude accrued fees from valuations, i.e. do not reduce the portfolio market value by the fee amount accrued.

Discussion The simple Dietz method is a variation upon the simple rate of return, which assumes that external flows occur either at the beginning or at the end of the period. The simple Dietz method is somewhat more computationally tractable than the internal rate of return (IRR) method. A refinement of the simple Dietz method is the modified Dietz method, which takes available information on the actual timing of external flows into consideration. Like the modified Dietz method, the simple Dietz method is based on the assumption of a simple rate of return principle, unlike the internal rate of return method, which applies a compounding principle. Also like the modified Dietz method, it is a money-weighted returns method (as opposed to a time-weighted returns method). In particular, if the simple Dietz returns on two portfolios over the same period are R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} , then the simple Dietz return on the combined portfolio containing the two portfolios is the weighted average of the simple Dietz return on the two individual portfolios: R = w 1 × R 1 + w 2 × R 2 {\displaystyle R=w_{1}\times R_{1}+w_{2}\times R_{2}} . The weights w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} are given by: w i = A i + C i 2 A 1 + A 2 + C 1 + C 2 2 {\displaystyle w_{i}={\frac {A_{i}+{\frac {C_{i}}{2}}}{A_{1}+A_{2}+{\frac {C_{1}+C_{2}}{2}}}}} .

Derivation The method is named after Peter O. Dietz. According to his book Pension Funds: Measuring Investment Performance,

"The method selected to measure return on investment is similar to the one described by Hilary L. Seal in Trust and Estate magazine. This measure is used by most insurance companies and by the SEC in compiling return on investment in its Pension Bulletins. The basis of this measure is to find a rate of return by dividing income by one-half the beginning investment plus one-half the ending investment, minus one-half the investment income. Thus where A equals beginning investment, B equals ending investment, and I equals income, return R is equivalent to

R = I ÷ 1 / 2 ( A + B − I ) {\displaystyle R=I\div {1/2}(A+B-I)}

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Simple Dietz method

Start with the simplest possible case. Write down what Simple Dietz method claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Simple Dietz method before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Simple Dietz method ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Simple Dietz method

In research: Simple Dietz method appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Simple Dietz method in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Simple Dietz method is common in secondary-school and first-year university syllabi. It links to neighbouring topics Finance theories, Investment, Mathematical finance, so understanding it makes those chapters shorter.
In everyday life: Look for Simple Dietz method outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Simple Dietz method in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Simple Dietz method means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Simple Dietz method out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Simple Dietz method in simple terms?

The simple Dietz method is a means of measuring historical investment portfolio performance, compensating for external flows into/out of the portfolio during the period. The formula for the simple Dietz return is as follows: R = B − A − C A + C / 2 {\displaystyle R={\frac {B-A-C}{A+C/2}}} where R {…

Why does Simple Dietz method matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Simple Dietz method?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Simple Dietz method.