Stocks for the long run?

Since leaving Facebook, I have been working on a bunch of pet projects that I have shelved for years. One of them  is particularly interesting (and useful for me) is to inspect historical investment returns with different asset allocation strategies. Being a statistician and knowing limits of the statistical methods, I dislike the way of characterizing risk as standard deviation in a lot of investment books.  The major issue I have with the standard deviation is that I feel the SD value  gives investors a qualitative/comparative measure of volatility but doesn’t really explain investment risks that well to investors. In other words, volatility is not the same as risk. As an investor, I am more interested in knowing the chance of losing money than knowing the volatility. What does a portfolio with annual return average = 8% and sd = 20% tell investors?  It certainly wouldn’t tell you that you can have a losing streak of -8%, -25%, -44% and -8% from 1929 to 1932 or -9% , -12% and -22% from 2000 to 2002 if you put all your money into S&P500.

Instead of using standard deviation, I would use the worst case scenario return as the measure of risk. I think it’s more comprehensible and investors can assess their risk tolerance by looking at the worst case returns and investment horizons at the same time. The conclusions from my analysis are not actually different from others but I personally feel I can make a better judgment on my risk tolerance based on the worst case scenarios. (I am probably totally re-inventing the wheels here but I feel more comfortable doing this before actually making a large amount of investment. So far, no investment advisers have shown me the data in such details.)

The following 5 data tables show the percentiles of inflation adjusted cumulative value of $1 invested in different stocks/fixed income allocations. The inflation data is based on CPI. The stock return data is from S&P 500. The fixed income portion is based on a mix of 50% T-Bills and 50% T-Bonds. I compared the portfolios with varying percentages of stocks. For example, if the stock percentage is 60%, it means the portfolio is 60% S&P 500, 20% T-Bills and 20% T-Bonds. I also include the “permanent” portfolio (25% T-Bonds, 25% T-Bills, 25% Gold and 25% stocks) for comparison. The data I used is from 1928 – 2010. I would love to do analysis with more detailed equity classes such as small-cap, international and value stocks but I couldn’t find a good source of free long term data online. (If you know where I can get them for a reasonable fee, please let me know.)

Table 1: 1-year inflation adjusted cumulative value

Percentage in Stocks \ Percentile 5th percentile 10th 25th 50th 75th 90th 95th
Permanent 0.92 0.96 0.99 1.03 1.08 1.13 1.15
0.00% 0.93 0.94 0.98 1.01 1.04 1.08 1.12
5.00% 0.93 0.95 0.99 1.02 1.05 1.08 1.12
10.00% 0.94 0.95 1 1.02 1.05 1.09 1.13
15.00% 0.94 0.95 0.99 1.03 1.05 1.1 1.14
20.00% 0.93 0.95 0.99 1.03 1.06 1.11 1.13
25.00% 0.92 0.95 0.99 1.03 1.07 1.12 1.14
30.00% 0.91 0.95 0.99 1.03 1.08 1.13 1.16
35.00% 0.9 0.94 0.98 1.03 1.09 1.14 1.17
40.00% 0.89 0.93 0.98 1.04 1.1 1.15 1.18
45.00% 0.88 0.92 0.98 1.05 1.11 1.17 1.2
50.00% 0.87 0.91 0.97 1.05 1.12 1.17 1.22
55.00% 0.84 0.9 0.97 1.07 1.13 1.19 1.23
60.00% 0.82 0.9 0.96 1.07 1.14 1.2 1.25
65.00% 0.81 0.9 0.96 1.07 1.14 1.21 1.27
70.00% 0.8 0.89 0.96 1.07 1.15 1.23 1.29
75.00% 0.8 0.89 0.96 1.08 1.16 1.24 1.31
80.00% 0.79 0.87 0.96 1.08 1.17 1.26 1.33
85.00% 0.79 0.86 0.96 1.09 1.18 1.27 1.35
90.00% 0.78 0.84 0.96 1.09 1.19 1.28 1.37
95.00% 0.78 0.83 0.96 1.1 1.2 1.3 1.39
100.00% 0.76 0.82 0.96 1.11 1.21 1.31 1.41

Table 2: 5-year inflation adjusted cumulative value

Percentage in Stocks 5th percentile 10th 25th 50th 75th 90th 95th
Permanent 0.89 0.95 1.10 1.18 1.29 1.38 1.43
0.00% 0.80 0.83 0.96 1.05 1.18 1.31 1.46
5.00% 0.82 0.85 0.98 1.08 1.20 1.33 1.43
10.00% 0.85 0.87 0.97 1.10 1.23 1.36 1.42
15.00% 0.87 0.88 0.98 1.11 1.25 1.38 1.42
20.00% 0.88 0.89 0.98 1.14 1.28 1.39 1.44
25.00% 0.88 0.90 0.99 1.16 1.30 1.41 1.50
30.00% 0.89 0.91 1.01 1.18 1.31 1.45 1.55
35.00% 0.89 0.92 1.03 1.20 1.32 1.50 1.59
40.00% 0.89 0.93 1.02 1.19 1.35 1.52 1.62
45.00% 0.89 0.94 1.02 1.20 1.39 1.58 1.67
50.00% 0.89 0.94 1.02 1.22 1.42 1.64 1.75
55.00% 0.89 0.94 1.03 1.24 1.46 1.70 1.84
60.00% 0.88 0.93 1.01 1.26 1.48 1.77 1.89
65.00% 0.88 0.92 1.00 1.31 1.52 1.81 1.95
70.00% 0.89 0.91 1.00 1.35 1.55 1.87 2.03
75.00% 0.88 0.89 1.00 1.37 1.58 1.92 2.12
80.00% 0.84 0.87 1.00 1.39 1.61 1.97 2.21
85.00% 0.80 0.86 0.99 1.41 1.64 2.00 2.30
90.00% 0.76 0.86 0.99 1.43 1.67 2.03 2.40
95.00% 0.72 0.84 0.98 1.44 1.70 2.07 2.50
100.00% 0.68 0.83 0.98 1.45 1.73 2.14 2.59

Table 3: 10-year inflation adjusted cumulative value

Percentage in Stocks 5th percentile 10th 25th 50th 75th 90th 95th
Permanent 0.86 1.05 1.25 1.39 1.52 1.66 1.72
0.00% 0.69 0.76 0.91 1.10 1.37 1.57 1.66
5.00% 0.73 0.78 0.93 1.16 1.43 1.59 1.72
10.00% 0.76 0.82 0.96 1.20 1.46 1.63 1.78
15.00% 0.78 0.87 1.00 1.24 1.51 1.70 1.83
20.00% 0.81 0.87 1.04 1.30 1.56 1.78 1.91
25.00% 0.84 0.87 1.07 1.36 1.59 1.87 1.96
30.00% 0.86 0.88 1.11 1.41 1.63 1.97 2.02
35.00% 0.86 0.89 1.13 1.45 1.74 2.03 2.08
40.00% 0.86 0.89 1.14 1.49 1.84 2.09 2.17
45.00% 0.88 0.90 1.14 1.52 1.91 2.20 2.28
50.00% 0.88 0.89 1.14 1.55 2.00 2.27 2.40
55.00% 0.88 0.90 1.19 1.58 2.09 2.39 2.54
60.00% 0.87 0.92 1.25 1.64 2.16 2.54 2.67
65.00% 0.86 0.91 1.29 1.67 2.21 2.70 2.80
70.00% 0.85 0.89 1.31 1.71 2.28 2.84 2.93
75.00% 0.84 0.88 1.29 1.74 2.35 2.96 3.09
80.00% 0.83 0.87 1.25 1.77 2.46 3.13 3.27
85.00% 0.81 0.87 1.27 1.80 2.60 3.30 3.44
90.00% 0.79 0.86 1.25 1.83 2.68 3.48 3.67
95.00% 0.77 0.85 1.25 1.87 2.79 3.65 3.90
100.00% 0.76 0.84 1.23 1.90 2.91 3.85 4.14

Table 4: 15-year inflation adjusted cumulative value

Percentage in Stocks 5th percentile 10th 25th 50th 75th 90th 95th
Permanent 0.96 1.08 1.37 1.6 1.82 1.96 2.11
0.00% 0.66 0.71 0.89 1.12 1.48 1.79 1.94
5.00% 0.73 0.76 0.91 1.21 1.54 1.9 2.08
10.00% 0.78 0.8 0.97 1.29 1.61 2 2.23
15.00% 0.82 0.86 1.06 1.35 1.68 2.1 2.4
20.00% 0.85 0.92 1.09 1.41 1.75 2.19 2.57
25.00% 0.89 0.95 1.12 1.45 1.86 2.28 2.73
30.00% 0.94 0.98 1.14 1.52 2.02 2.38 2.88
35.00% 0.97 1.02 1.18 1.61 2.13 2.48 3.03
40.00% 0.98 1.07 1.28 1.7 2.26 2.57 3.19
45.00% 0.98 1.1 1.34 1.79 2.42 2.76 3.37
50.00% 0.99 1.11 1.4 1.96 2.56 3.04 3.56
55.00% 0.99 1.15 1.43 2.04 2.74 3.32 3.75
60.00% 0.99 1.16 1.44 2.08 2.94 3.56 3.98
65.00% 0.99 1.17 1.45 2.19 3.16 3.87 4.25
70.00% 0.99 1.18 1.46 2.31 3.31 4.17 4.55
75.00% 0.99 1.15 1.47 2.42 3.46 4.53 4.93
80.00% 0.99 1.12 1.53 2.55 3.75 4.93 5.31
85.00% 0.99 1.09 1.56 2.67 4.02 5.29 5.7
90.00% 0.99 1.07 1.58 2.79 4.25 5.73 6.14
95.00% 0.99 1.06 1.62 2.9 4.65 6.19 6.67
100.00% 0.97 1.06 1.66 2.97 4.93 6.71 7.16

Table 5: 20-year inflation adjusted cumulative value

Percentage in Stocks 5th percentile 10th 25th 50th 75th 90th 95th
Permanent 1.14 1.2 1.49 1.81 2.19 2.42 2.46
0.00% 0.68 0.7 0.87 1.09 1.65 2.1 2.32
5.00% 0.76 0.78 0.97 1.15 1.75 2.25 2.51
10.00% 0.85 0.87 1.03 1.27 1.84 2.41 2.67
15.00% 0.94 0.98 1.08 1.35 1.93 2.58 2.86
20.00% 1.04 1.07 1.18 1.44 2.02 2.76 3.1
25.00% 1.1 1.12 1.25 1.64 2.11 2.95 3.35
30.00% 1.13 1.19 1.37 1.81 2.34 3.15 3.62
35.00% 1.16 1.22 1.45 1.88 2.47 3.35 3.91
40.00% 1.18 1.25 1.51 1.95 2.62 3.58 4.22
45.00% 1.21 1.27 1.57 2.08 2.86 3.77 4.56
50.00% 1.25 1.29 1.65 2.3 3.14 3.98 4.92
55.00% 1.28 1.31 1.71 2.48 3.44 4.22 5.24
60.00% 1.3 1.34 1.76 2.68 3.69 4.61 5.57
65.00% 1.3 1.38 1.8 2.86 3.92 5.03 5.93
70.00% 1.31 1.41 1.85 3.07 4.32 5.48 6.32
75.00% 1.33 1.43 1.91 3.34 4.74 6.12 6.73
80.00% 1.35 1.45 1.96 3.62 5.08 6.82 7.18
85.00% 1.37 1.47 2.01 3.89 5.3 7.32 7.96
90.00% 1.39 1.48 2.05 4.21 5.77 7.84 8.87
95.00% 1.41 1.5 2.09 4.55 6.05 8.39 9.8
100.00% 1.42 1.5 2.13 4.91 6.39 9.2 10.65

There are 3 major points from the above tables.

  1. Stocks are for VERY VERY long run. If you are tempted to put 100% of your portfolio into stocks because its average superior returns compared to fixed-income securities, think twice. If your investment horizon is less than 15 years, the cumulative values of an all stock portfolio at 5th and 10th percentiles are less of some more modestly allocated portfolios . In other words, there’s a pretty good chance (~10%) that your all stock portfolio will under perform the more modest 50/50 equity/fixed-income portfolios. You will have to ask yourself that if you are able to stomach such depressing returns in a fairly long investment horizon (like 15 years). Furthermore, you might think 10% is not a very high chance, but it really means once every 10 years. Most investors like you and me probably still have a few more decades to live. In their life time, they are very likely to hear from the press a few times on how terrible long term stock returns are. If investors react to the press and sell, they probably will sell precisely at the bottom. The 20 year cumulative returns show that an all stock portfolio beat all other portfolios across the board.  But the real question is “Can you wait that long?”
  2. You have to own some stocks to beat the inflation. If you are risk-averse and are tempted to have a 100% fixed-income portfolio, DON’T. Inflation is going to catch up with you(r portfolio). There’s only a 50% chance that your portfolio will hold up to inflation after 20 years (with cumulative value >$1). And, that’s while you are not withdrawing any money from the portfolio, which is an unlikely scenario since you probably have to pay tax from your income. I am working on another article regarding withdraw rates but the main takeaway here is that an all fixed-income portfolio is risky in the long run.
  3. A mix of equity/fixed-income portfolio is less risky than the all fixed-income portfolio. If you look through all the data tables, you will probably notice that the cumulative value of 100% fixed-income portfolio is less than other moderately risky portfolio across all investment horizons and all return percentiles. It might be counter intuitive but according to the historical return data, a 50%/50% equity/fixed-income allocation is less risky than a 100% fixed-income portfolio as long as your investment horizon is not too short (like 1 year).

As for the permanent portfolio, it seems to be less risky and have better long term return than a 25%/75% equity/fixed-income allocation. For really really conservative investors, I think it might be a good choice.

Finally, I want to point out that no matter what asset allocation you pick, there’s still a non-trivial chance that you would not make any money in pretty long investment horizons (like 10 or 15 years) after adjusting for inflation. Personally, I am not too worried about it because it’s not just me losing money. If almost everybody loses money on their investments, as long as I lose relatively less, I am still ahead.

Personally, I will have a 60%/40% equity/fixed-income portfolio since the worst case scenarios are pretty acceptable to me and the long term return is fairly decent. The next step is to make sure the plan is well executed and well maintained going forward. I will share my experience on how I selected my advisers in another article.

Update 1: A number of people pointed out that the numerical analysis of historical return is dangerous as there are not that many data points available. (In fact, I only have 83 points.) Plus, using the stock returns for the United States in 20 century to predict future returns is probably overly optimistic. I agree that we may not see the returns that will match the 20th century but I don’t have a strong reason to believe that the relative return of stocks vs. fixed income will be dramatically different over the long run. After all, stocks represents a real ownership of a company while fixed-income is a “you-owe-me” agreement that only represents a small portion of value created by the economy.  I believe the conclusions would still hold but I will use a larger data set to confirm.

Update 2: I use Robert Shiller’s dataset from 1871-2010 to redo the analysis. Please see the spreadsheet for more details and comparisons. All the conclusions above still hold. The 100% fixed income rate survival rate improves a bit ( from 50 % to 60%). Maybe that’s because Shiller’s dataset is not using the 3 month T-Bill but the 1-year interest rate.  Considering tax, I would definitely not put 100% portfolio into fixed-income. If you are really really conservative, put 25% of your portfolio into equity classes will help you reduce risk and survive inflation. Someone mentioned using TIPS to beat inflation while preserving purchasing power. I think TIPS is great when it’s paying 2-3% interest. But now TIPS is paying 0%. If you buy TIPS right now, you will have negative after-tax real return at least until it matures. I will probably own small percentage of TIPS as part of the fixed income allocation. I am not sure it’s a very good strategy to own a majority of the portfolio in TIPS at the moment. It’s basically betting on inflation.

Appendix:

Here is some information about my data source and more detailed data on the returns and return percentiles.

Here is the spreadsheet I used for annual return data after consolidating from the following sources

Here is the spreadsheet with detailed cumulative return and percentile data computed from the above spreadsheet

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