Option 2, 2 bond funds, 2 stock funds, and a 50/50 balance fund.
Money market, long term US bonds, S&P 500, NASDAQ, and
then this balance fund, which is 50% stocks, 50% bonds.
Option 3, 2 bond funds, 4 stock funds, so money market funds,
long-term US bonds, S&P 500, NASDAQ.
Then we have a large stock fund and a growth stock fund.
So you can see these options have different funds in them,
but they all kind of have the same type of investments available.
Like Money Market and short term US Bonds are kind of similar investments,
as are long term US Bonds and medium term US Bonds.
Growth Stock Fund and NASDAQ would probably perform somewhat similarly,
S&P 500 stock fund, and a large stock fund,
S&P 500 is large stocks, would also perform similarly.
So as we go from the 2 bond funds to the 4 bond funds,
it's not like our investment opportunities have really expanded that much.
The same as you go from 2 stock funds to 4 stock funds.
It's not like our investment opportunities have expanded that much.
So you really can get the same, I would guess,
reward to risk trade-offs across all three of these plans.
Okay, so what are the hypotheses, if we're looking at these three plans,
Option 1, Option 2, and Option 3?
If the agents are perfectly rational, we would expect them,
out of equity investment across the three plans, to be roughly the same, right?
Because they all have basically the same investment opportunities in the bond
space, in the stock space.
In a behavioral finance perspective, naive diversification would say,
as we look at Option 3, you're going to see more investment equities,
because there's simply more stock funds.
When we go to Option 1,
we're going to have more investment in bonds Because there's more bond funds.
Okay, so what are actually the predictions that we would see as in terms of
the percent of the assets invested in equity or stocks across these three plans.
Well the rational agent predictions see if we give these plans to people randomly,
we should see on average about the same equity allocation across all three plans,
okay?
Now the behavioral or naive diversification prediction is
we should see a dramatic change in the equity allocation.
We're going to see much more stock investment in the plan that has 4 stock
funds and much less in those that only has 2 stock funds.
Now I've done this experiment here many years for the MBA and MSF audience,
it kind of works like clockwork.
That you'll see this Option 3, people that were given this will invest about
30 to 35% more on stock than those that are granted plan 1.
Now, when I do it with an executive MBA group, I see smaller differences.
There still might be a slight tilt toward more equity and
plan 3 here that has 4 stock funds but the difference relative to the plan that
has two stock funds might only 10% each points, as supposed to the 30% or 35%.
But of course, the executive MBA group is a very select audience with a lot of
financial experience.
So it's not surprising that they may be less subject
to this naive diversification bias here.
So you can also think, besides looking at this experimentally, to look at
the mix of options and allocations and contributions for actual plans, okay?
So in the work that I have done with Jeff Brown and Nelly Liang we examined the data
for roughly 1000 publicly traded companies over 1991 to 2000.
We're going to look at the type of plan options provided by the firm, like your
own company stock, US equity funds, bond funds, international funds, etc.
Then we're also going to look at the investment decisions of participants.
How do they allocate their own contributions across these various funds.
And in particular, how does a contribution of plan funds,
which is the firm decision, how many stock funds, how many bond funds.
And the composition of allocation investment decisions,
which is decided by the worker.
How does that vary with the number of options in the plan?
So let's look at some of these results here, and
we're going to look at this by investment options.
So first we're going to look at fund options and
contributions for employer stock.
The, I guess, purple line here with the diamonds is showing the share
of fund options as a total number of options in the plan griows.
So company stock by definition is one option.
So if there's four options in the plan, 1 over 4 is 25%.
If there's 10 options in the plan, 1 over 10 is 10%, okay?
So not surprisingly, if there's more options in the plan,
the share options that are company stock is declining.
Okay, that's a definition.
How about the share of contributions?
Now this is controlled by the participants.
How much do you invest in company stock?
You can see this is the pink line with the squares here.
So you can see that as you increase the number of options in the plan,
you see participants are investing less in company stock.
That would be consistent with a naive diversification.
I put more in company stock if it's 1 out of 5 options than if it's 1 out of 10.
So how you set up the plan actually influences a company's stock investment.
And if you have more options in the plan,
people tend to invest less in company stock.
Now you can see this pink line is above the purple line.
That could actually represent familiarity bias, right?
Like controlling for how many options there are in the plan.
We see people investing more in company stock
than the simple naive diversification prediction.
That could just represent the familiarity bias
that causes people to like to invest in company stock.
But what's interesting is the share of investment to company stock is declining
as there's more options in the plan.
Now how about domestic equity fund.
So this is where we're talking about a sample of US pension plans.
So this is looking at investment in US stock funds.
So interesting pattern here, as the plans get bigger with more options,
the share of options that are equity funds actually increases.
And this is a choice by the firm.
So, if you have 5 options About 30% are stock funds, excluding company stock.
Right, our broad stock funds.
You get up to, 12 plus options almost 50% of the choices are stock funds.
So as the plans get and bigger,
the marginal investment option added as a stock fund.
Well what does that lead to?
Well you see that as the plans get bigger with more options,
not only are the share of options in the plan that are stock funds increasing.
So are contributions from participants to the stock funds.
So there's an adding up constraint.
If the share of funds and the share of allocations of contributions to stock
funds is going up as the number of options in the plan goes up, for bonds,
you have to have a declining relationship, right?
because everything has to add up to 100%.
So as the number of options in the plan increases,
the share of fund options, this purple line with the diamonds,
that are going into fixed income funds, is declining.
If you have 5 options in the plan, 35% of the options are fixed income or
bonds, it's only 25% if you have 11 options in the plan.
