economics personal-finance

# Thoughts on Optimal Investment

## The Efficient Market Hypothesis

Generally speaking, there are two types of investment: active and passive. Active investing entails spending time/money/effort to find good investments and good times to buy/sell to optimize your risk-adjusted rate of return, while passive investing entails buying one or more index funds and just continuously buying each month.

There is, admittedly a continuum to be seen here, but, by and large passive investment tends to be as good as (if not superior to) active investment within an asset class for the majority of people Passive management. This hypothesis is backed up by historic data, since low-fee index funds have outperformed most funds actively managed by investors Liu. All of this supports the idea that financial markets are generally efficient and trying to "beat" them is typically foolhardy.

All that being said, the fact that financial markets are typically efficient is not a slam-dunk argument against applying intelligence to investment. In particular, there is good evidence markets are not efficient between countries Equity home bias puzzle Backus–Kehoe–Kydland puzzle Feldstein–Horioka puzzle. Moreover, different utility functions (i.e. risk aversiveness) imply different asset class mixes in some pretty significant ways. For instance, as I discuss later, the only people who buy treasury bonds are people who are extremely risk averse - or rather people who think they're extremely risk averse because they're bad at understanding risk quantitatively. What's more, there's at least some evidence the EMH doesn't really apply across asset classes.

For these reason, I'm not going to talk about how to choose which particular stocks/bonds/etc to invest in. Instead I'm going to discuss the other aspects of investing: which indexes to use, how to allocate your savings between those indices to balance risk and return, and how to avoid large tax bills. If you're instead interested in "beating the stock market", a place to start is this dataset Marjanovic.

## Taxes

Any American who wants to understand optimal investment should have a solid understanding of the US tax code. I've listed the most important topics below, but this list isn't meant to explain any of these in-depth; it should instead be viewed as a good point to start your own research.

1. Tax Advantaged Accounts - principally 401(k)s and IRAs Comparison of 401(k) and IRA accounts but also HSAs and FSAs. After maxing out these contributions, you can save even more tax-advantaged money via the "mega backdoor" conversion Mega Backdoor Roths: How They Work Technically, your house can be a tax-advantaged investment in that your mortgage interest may be tax deductible.
2. Short Term Penalties - there are two main ways holding investments short-term is penalized by the US tax code. First, generally speaking, selling an asset less than a year after buying it will result in it being taxed as ordinary labor income. If you hold the asset for more than a year, it is generally taxed at the lower capital gains rates Topic No. 409 Capital Gains and Losses. Similarly, dividends are taxed as ordinary labor income by default, but if (a) you hold the stock for at least a couple months and (b) the stock is for a US corporation, then you can generally pay the lower capital gains rates Qualified dividend.

## Pre & Post Retirement

All this analysis has assumed you have a fixed nest egg that you are neither adding money to nor withdrawing money from.

If you are still contributing money to your nest egg, then you are even more risk tolerant than our simple model investor, which makes the risky S&P 500 even more attractive relative to safe bonds and housing than the above analysis considered.

To determine the optimal asset allocation in retirement, I determined which allocation would have allowed you to withdraw the most fixed amount of money per year (in real terms) without ever running out historically after 40 years - a number knowing as the safe withdrawal rate (SWR). Given the 5 above investment options, the best allocation is 39% housing and 61% housing - an allocation with a SWR of 5.3%. Note, the S&P 500 alone has a SWR of just 4.2%, so this is a significant improvement.

We can do a bit better by changing our allocation over the course of our retirement. In particular, by starting at (0% sp500, 100% housing) and shifting to (80% sp500, 20% housing) over the 40 years, our SWR increases to 5.6%.

The reasoning behind the reversal is that how you do in retirement depends a great deal on when the market moves. In particular, two decades of steady growth followed by a huge drop is much better for you than a huge drop followed by two decades of steady growth (you can prove this to yourself by using a toy example). That's why optimal asset allocation is to hold safe investments during the early parts of your retirement and shift to riskier (i.e. higher income) growth later on.

Note: this recommendation goes against conventional financial wisdom which generally says to invest more conservatively as you grow older.

## Summary

• Learn how to avoid taxes.
• While saving for retirement, invest your money solely the SP500 and housing, probably with an emphasis on the former.
• After retiring, you can probably safely withdraw around ~5% of your initial assets each year (adjusting for inflation) if you start investing exclusively in housing and shift towards a more S&P 500-focused portfolio as you age.

## Future Lines of Inquiry

• Investigate how skew affects the formula instead of kurtosis.
• Investigate how uncertainty in the estimated covariance matrix affects optimal asset allocation. A good jumping off point is Wishart distribution.
• This paper Fundamental Credit Special has a table of decade-based US corporate bond returns back to 1900 on page 10. They also have a graph that strongly suggests the authors have access to annual returns, but I can't find them on the internet. They claim corporate bonds have averaged 2.2% real annual returns sine 1900. This is barely better than treasury bonds (1.5%), so I doubt non high-yield "junk" bonds are a sensible investment. As a sanity check on their data, they suggest equities have averaged 6.0% real returns, which is virtually identical from the returns given by Macrohistory. The other data I found on the topic was a graph of overall bond yields going back to 1926 When will we get back to average market returns. I've included that data (transcribed to numeric form) in the aforementioned spreadsheet. It generally also finds quite low returns (~2.5%), which confirms my general feeling that bonds are a poor investment.
• I need to include international financial markets in the analysis. I recall seeing a dataset that cost a lot of money that had international returns going back about a century. I'm not willing to drop thousands of dollars on this, but this suggests that international returns also go back a long time - I just need to find them.