Wednesday, April 26, 2017

Measuring Returns for Different Investment-Consumption Patterns

Measuring Returns for Different Investment-Consumption Patterns

Question:   An investment advisor tells his client to invest $1,000 per month in VFIAX (Vanguard S&P fund) for five years.   The person will then live off the proceeds in this fund for 36 consecutive months.  

Calculate the return on assets from this investment/consumption plan for two different start dates – January 1, 2002 and January 1, 2003.

What is the NPV of investment returns from this investment strategy/ consumption plan on the same start dates?

What should investors who are planning to save for five years and spend for three years learn from this example?

Mutual funds and ETFs tend to advertise holding period returns based on specific purchase dates and specific sale dates.   These returns are based on the price of securities on two dates only.   What does the example presented here tell you about the usefulness of two-period return statistics reported by mutual funds?  

Methodological Note:  The shares purchased each month are $1,000/PVFIAX where PVFIAX is the price of the ETF.   I sum over 60 months to get the total shares purchased, which I will denote TSHARES. The formula for cash inflow for the 36 months are (1/36)*TSHARE*PVFIAX.

The cash inflow/outflow column and the date column are inputted into the XIRR function in Excel to give the IRR of the inflows/outflows on these particular dates. The XNPV function gives net present value of the cash flows.

An appendix to this post lists the data used in the XIRR and XNPV calculations.


The value of VFIAX reached its pre financial crisis high in 10/2007 and reached its crisis trough in 02/2009.   Hindsight is 20/20 but it appears as though diversification prior to the downturn would have been beneficial.

What follows are return calculations for the two scenarios.

Results are in the table below.

Returns for Two Investment/Consumption Scenarios
Invest Period
Consumption Period


·      The person who stopped saving in December 2006 did fairly well despite the financial crisis.   The IRR for this investor was 12.04 %.   The NPV of the investments was $15,766.   (NPV calculation assumes a5 percent cost of capital.)

·      The person who stopped investing in December 2007 realized a return only slightly higher than 0 percent.  The NPV of this person’s investment was around $800.

Discussion of Investment Strategy:

In my view, a 100 percent VFIAX strategy is unwise for an investor with this type of investment and consumption period.

How to fix this problem is a more difficult question.  It is important to note that the strategy of putting 100 percent of funds in VFIA for an investor with a start date of January 1 2009 or January 1, 2010 did quite well.

529 plans offer life-cycle funds that drift towards a more conservative investment as the person nears the date where he must spend money.   Lifecycle funds would have done reasonably well for both of the scenarios considered here.  However, the life-cycle approach creates miserable results when the market does poorly in the first few years of the investment period and then rebounds.

My view on how to solve this problem is evolving.  A 60/40 (stock/bond) portfolio would have done well in these time periods but I don’t believe that it will work in the next crash.  Interest rates are now very low and I expect in the next crisis bonds and stocks will crash together.   Perhaps allocating some resources into an inflation-indexed bond fund would help balance returns during the next crisis.

The trend in investment is toward investment in passively managed funds like the ones offered by Vanguard.    This is at best a partial solution.   Investors need help in allocating money across several passively managed funds.  This includes advice on initial allocations and reallocation over time.

I believe there is a need for an actively managed fund that invests exclusively in passively managed funds and reallocated assets across funds as market conditions change. 

Note on traditional holding period statistics:  The value of VFIAX in January 2002 was 17.9.  In December of 2010 the value of VFIAX was 39.5.   The return for this 7.9 year  holding period was at 10.5%.

Holding Period Calculation
Holding Period in Years

However a person who started investing in January 2003 and started spending in January 2008 earned squat!  

The mutual funds can legally and honestly report great eight-year or ten-year holding return but their clients aren’t doing particularly well.

Such a surprise!  

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