A challenge: Recommend an asset allocation

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A challenge: Recommend an asset allocation

Postby MrMatt2532 » Wed Jan 23, 2013 12:41 am

Intro
In choosing an asset allocation, it is often recommended to assess one's ability, willingness, and need for market risk as per Larry Swedroe.
Ability for market risk is determined by your financial circumstances.
Willingness for market risk is determined by an investors fortitude for risk.
Need for market risk is determined by an whether an investor needs to take risk. (Have they already won the game?)

Most investors know that factors such as job security, savings rate, time horizon, debt, current portfolio value, future pensions/social security, and other financial circumstances all contribute to one's ability to take risk. Bogle recommends to use age in bonds (including a pension/social security in the bond value). This model accounts for time horizon and pensions/social security, but doesn't make an attempt to account for much else. So, you might use that recommendation as a starting place and adjust from there considering your other financial circumstances. The question is how? Personally, I don't see an obvious way to do it. We know holding debt decreases our ability to take risk. We know high job security increases our ability to take risk. The question is how can I quantify these various circumstances?

The Challenge
Below I have a spreadsheet showing 16 different investors. They are all 50 years old and are retiring in 15 years. There are two levels of financial assets(300k/600k), two levels of debt (0/200k), two levels of pensions (0/100k), and two levels of savings rates (10k/30k). Assume the debt is at a low rate, potentially a mortgage (not necessarily though). The savings rates are expected to grow with inflation. The 16 investors make up the 16 combinations of those cases (2^4). I also include the average investor as a 17th case. My challenge for you is to recommend how to allocate the financial assets between stocks and bonds for these different investors. We need to assume something about willingness. Let's assume that these investors have the willingness to expose their expanded assets (financial assets+human capital+pensions-debt) to the risk of a 40/60 stock/bond portfolio. Note that I believe it is at this expanded level that risk should be determined. A proof of sorts: if you made 1M a year and you have 5M in a government pension, I bet you would be able to sleep at night even if you had a 100%/0% stock/bond portfolio valued at 2M. Also note that we don't know anything regarding the investor's expenses/future expenses. In addition, the expenses aren't necessarily the same for these 17 investors. This recommendation for stocks/bonds will only be made using the investor's willingness and ability to take market risk. Afterwards, the investor's need for market risk can be considered.

The Investors
Image
Note: average represents an average case investor (17th case)

My Approach
One of the fundamental reasons that we choose greater stock allocations when younger (a la 'age in bonds') is that we have greater human capital when younger and less when older. What I'm recommending is not to just recognize this qualitatively, but to actually utilize this in choosing an asset allocation. To calculate the human capital, I will find the discounted sum of the future expected savings (income-consumption). For the discount rate I will choose at a minimum the risk free real rate of return on a 15 year bond (around 0%). Due to potential uncertainty in my earnings and job security, I will discount by 3% and treat the human capital as a bond. The formula is HC=S*(1-1/(1+i)^n)/i, where HC is human capital, S is savings rate, i is the discount rate, and n is the time horizon. The pension value is also found by finding the discounted sum of all future income streams from that pension. Consider the pension properly discounted and treat it as a bond. Debt is considered a negative bond. Now my expanded assets will be equal to financial assets+pension+human capital-debt. The financial assets are my financial portfolio that i'm trying to allocate between stocks and bonds.

My Solution vs 'age in bonds'
Image
Note1: average represents an average case investor (17th case), not an average of the above
Note2: the first % stocks column is my solution and the second is bogle's 'age in bonds'
Note3: steps to calculate 'age in bonds' stocks%: Take investor 2. Financial assets+pension=400k. Age in bonds for a 50 year old, so 50% stocks/50% bonds, so stocks are 200k. Therefore, stock allocation should be 200k/300k = 67%.
Note4: steps to calculate stock% in my method: Take investor 2. First calculate human capital. HC=10*(1-1/(1+.03)^15)/.03=119k. Now expanded assets are financial assets+pension+human capital-debt=519k. Willingness was decided to be that of a 40/60 stock/bond portfolio. Therefore, stocks=.4*519=208k. Therefore, stock allocation should be 208k/300k = 69%.

Discussion
In analyzing the results, we make several observations:
1: Increased debt decreases one's ability to take risk
2: Increased savings rate increases one's ability to take risk
3: Increased pension increases one's ability to take risk
4: Generally, increased financial assets decreases one's ability to take risk (depends on relative values of other assets)
5: My results have a correlation of .38 with 'age in bonds' results
6: The average stock/bond ratio recommended is 59% by my approach and 57% by bogle's approach (good comparison). This refers to averaging all the cases, not the average investor. Worth noting: the fact that the average investor compares well with the average of all the cases tells us that interpolating in this operating domain you would expect a linear interpolation to be a good one.
7: The standard deviation of the difference between my approach and bogle's approach is 17%. As mentioned, we see that on average bogle's recommendation does a good job in recommending an asset allocation, but it can have large errors from not accounting for debt/savings rate
8: It is worth noting that it should be easy to factor in debt to the 'age in bonds' approach, but practically this makes no sense for a young investor. It would recommend 0% or a very low percentage in stocks, and therefore I don't believe 'age in bonds' assumed factoring in debt.

Most of these results are not unexpected, but the advantage of my approach is that it gives you a quick and easy way to quantify your financial circumstances. There are certain cases where my approach recommends a much different stock/bond mix than the 'age in bonds' approach. Let's discuss two: The largest difference is for investor 3, where 'age in bonds' recommends 50% stocks, and my approach recommends 88%. The reason for this is that this investor has a low amount of financial assets and is saving at a high rate. This is a similar situation to a young investor with little in financial assets but has a lot of human capital, for which we would recommend a high stock percentage. The second largest difference is investor 6, where the investor can't save very much per year and has a lot in debt, therefore doesn't have a high ability to take risk. In this case, 'age in bonds' recommends 67% stocks and my recommendation recommends only 43%.

Ideally, an investor would adjust for all of the relevant financial circumstances involved in determining an asset allocation. If one follows an 'age in bonds' approach without actually making the proper adjustments, they are inherently making a bunch of potentially bad assumptions about how much they have, how much they save, how much debt they have, and so on. The same could be said about a user of 'target date' funds. These funds will assume you are some generic investor retiring in 20XX. I see this as a potential issue, and I thought it was worthwhile to present this more systematic approach here that actually is personalized for your unique financial circumstances.

Finally: Assessing Need
At this point the investor can assess need for market risk. All of the asset allocations that I recommend essentially have the same risk profile viewing from the expanded assets level (financial assets+pension+human capital-debt). We would have to know something about the consumption level/expenses for each investor to make this final adjustment to the asset allocation recommendation.
Last edited by MrMatt2532 on Wed Jan 23, 2013 12:08 pm, edited 2 times in total.
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Re: A challenge: Recommend an asset allocation

Postby letsgobobby » Wed Jan 23, 2013 1:44 am

I just meditated for a while and a vision of 60/40 sorta flittered into my mind... And that's where I've stayed.
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Re: A challenge: Recommend an asset allocation

Postby learning_head » Wed Jan 23, 2013 9:35 am

Very nice post MrMatt! Makes sense to me.
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Re: A challenge: Recommend an asset allocation

Postby Rodc » Wed Jan 23, 2013 10:14 am

Didn't we just have this discussion?

viewtopic.php?f=10&t=109353&p=1590560#p1590560
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Re: A challenge: Recommend an asset allocation

Postby MrMatt2532 » Wed Jan 23, 2013 10:25 am

Rodc wrote:Didn't we just have this discussion?

viewtopic.php?f=10&t=109353&p=1590560#p1590560

Sort of. That post and discussion got a bit sidetracked. My original post didn't focus on implementation so I don't think anybody could see the usefulness in what I suggested. Additionally, almost all the discussion was focused around mortgages/negative bonds/home equity. I wanted to shift the focus away from that and focus on the general process of considering willingness, ability, and need in choosing an asset allocation.
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Re: A challenge: Recommend an asset allocation

Postby larryswedroe » Wed Jan 23, 2013 10:06 pm

Just a few quick thoughts as am busy.

Some key concepts that should be thought of is the volatility of the labor capital, sometimes it's like a bond (say a tenured professor) and sometimes very stock like (say an automobile worker)

Another key concept I think was missing was the marginal utility of wealth, which impacts the need and willingness to take risk, and can outweigh other factors.

And one should consider what options one has if the left tail risk shows up. More acceptable options (like ability to work longer or cut expenses), more ability to take risk

These issues are all discussed in The Only Guide You'll Ever Need for the Right Financial Plan

Without considering them, one cannot make a good recommendation.
Best wishes
Larry
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