A long-term investment strategy using the Nikkei average

Published on February 1, 2015

A long-term investment strategy using the Nikkei average

On this page we think about long-term investment using the Nikkei Stock Average from 1970 onward.

The Nikkei average was 2,402 yen on January 5, 1970, and 17,451 yen on December 30, 2014 (source: Nikkei Stock Average Data Room). This means that if you had kept investing in line with the Nikkei average, you would have made a 626% profit, which works out to an annual return of 5.8%.

Investing in stocks is on average positive, but this high rate of return is also thanks to the (largely unrepeatable) rapid economic growth and the bubble economy. On the other hand, events such as the collapse of the bubble and the Lehman shock can also turn the return negative.

Investment carries risk, but considering that consumer prices in 2014 had risen to 3.10 times their 1970 level (source: Consumer Price Index, All Items (base index)), simply holding yen also carries risk.

So we consider a way of investing in the Nikkei average that avoids losing assets during recessions as much as possible while still making a profit when possible. Using the daily data from the Nikkei Stock Average Data Room, we look for an investment method that can be expected to make a profit going forward.

The basic strategy

In long-term investment, trend-following (predicting that the price will keep rising or keep falling in the same direction as it is currently moving) is said to be effective. So we consider a trend-following strategy that buys (or keeps holding) the stock when the current price is at least X% above the average price over the past Y days, and otherwise sells (does not buy). (We use "the average of the past Y days' average prices" rather than "the average price Y days ago" because the former reduces noise and also reduces the number of trades.)
Figure 1: The trend-following strategy
(the state where the price is X% above the average price over the past Y days)
Figure 1 shows the two parameters of the trend-following strategy. X represents the rate of increase over the average price, and Y represents the number of days referenced. If you set the threshold X high, you can hardly trade at all, making losses less likely but pushing the return toward 0%. If you set it low, you are always invested, which approaches the 5.8% annual return shown at the beginning, but you cannot cope with the risk of a recession. Making Y large reduces the number of trades but makes it harder to demonstrate the stability of the method. Making it small increases the number of trades but makes it easier to demonstrate stability.

Results of applying the trend-following strategy to the Nikkei average

Figure 2 is a heat map of the result of comparing today's average price with the average price over the past Y days, buying (or keeping) the stock when it is at least X% higher and selling (or not buying) otherwise.
Figure 2: Average return from 1970 to 2014
(The lower bound is multiplied by the square root of the number of years referenced. For example, when the number of referenced days is 1, it shows the range ±50%/√365.0. This is an adjustment based on the fact that the magnitude of fluctuations in prices and the like is proportional to √time.)
The highest value was achieved when buying if today's price was at least 0.74% above the average price over the past 24 business days, yielding a 1655% profit (8.5% annual return). We can see that a trend-following strategy with a threshold X near 0% and a number of referenced days Y of at least a few weeks was effective over this period.

Stability across decades

When dealing with time-series data, using only the result over the entire period as in Figure 2 tends to cause a kind of overfitting and is very dangerous (for example, finding a method that makes big money only during the bubble is a poor choice for future use). So we first split the results by decade and check that no single period has an extreme influence on the overall result.
Figure 3-a: 1970–1979
Figure 3-b: 1980–1989
Figure 3-c: 1990–1999
Figure 3-d: 2000–2009
Figure 3-e: 2010–2014
The parameters with the highest rate of return, and the average annual return, were:
  • 1970s … days: 1, lower bound: -0.05%, annual return 24.7% (Nikkei average's annual return 10.6%),
  • 1980s … days: 1, lower bound: +0.15%, annual return 25.5% (Nikkei average's annual return 19.4%),
  • 1990s … days: 22, lower bound: +2.38%, annual return 7.6% (Nikkei average's annual return -6.9%),
  • 2000s … days: 66, lower bound: +2.06%, annual return 5.8% (Nikkei average's annual return -5.6%),
  • 2010s … days: 5, lower bound: -1.77%, annual return 16.1% (Nikkei average's annual return 5.0%).
Even in the 1990s and 2000s, which were periods of recession, we can see a tendency for the annual return to be positive around where the lower bound is 0. From Figure 3 we can see, in every decade, a tendency for the annual return not to become small around where the lower bound is 0. This shows that the trend-following strategy may be able to mitigate the risk of recessions.

Day-to-day stability

Now that we know it is good to set the lower bound near 0, we next look at how the day-to-day investment performance changes as we vary the number of referenced days. By looking at the stability of the day-to-day investment performance, we can gauge the degree of risk.
Figure 4: Day-to-day change in assets, with January 1, 1970 set to 1
It shows the change in assets for the Nikkei average and for reference-day counts of 1, 20, and 100 days.
Because only the 100-day reference count keeps making a profit consistently even after the collapse of the bubble, we can see that a longer reference period avoids large losses during recessions. On the other hand, a longer reference period dulls the response, so it may fail to keep up with the movements of the Nikkei average, as around 1989.

Future work

This page does not account for the fees associated with trading. It also does not discuss how the "expected value of profit" is calculated.

Appendix