Investing Large Sum of Money: Part 2

In the previous post of this series, I looked at how the return per unit of risk of a Dollar-Cost-Averaging strategy to investing a large sum of money has historically been lower than a Lump-Sum strategy. In this post, I would like to look at another risk metric, maximum drawdown, to see if DCA adds value in this regard.

If you’re new to the term, drawdown, find the definition here. It is basically the difference between the peak value recorded of an investment and a subsequent trough value recorded during an investment horizon.

Intuitively, it makes sense that spreading out investment over a period of time would reduce drawdown since the uninvested portion of the initial cash would not incur any loss. Let’s see how the two different strategies performed in SPY for the past 25 years.

First, take a look at the price chart of SPY in the year 2010.

If I had $10K to invest on Jan 1, 2010. The following chart shows the change in the value of the two accounts.

The red portion of the line shows the maximum drawdown period. In this particular example, the maximum drawdown realized of the Lump Sum strategy is $1694.39 whereas that of the DCA strategy is $662.24. As expected, DCA significantly reduced the maximum drawdown of the investment.

Below, I plotted the histogram of $-maximum drawdowns in the 25-year history.

As expected, we can see that DCA can reduce the magnitude of drawdown, mostly due to the uninvested cash sitting idle.

Intuitively, DCA seems like a less risky investment strategy than Lump Sum (LS). One might have thought that Sharpe ratio of DCA would be higher than that of LS. We showed using the SPY chart that it was not the case. DCA did, however, reduced the drawdown due to the fact that there were uninvested cash impossible to incur a loss.

For investing in SPY, my conclusion would be that Lump Sum has been a much better investment than DCA. It is simpler to implement (1 transaction rather than multiple) and it has higher Sharpe Ratio. The good thing about DCA is that it can reduce drawdown; however if your main goal is to reduce drawdown you can just reduce the aggregate investment amount. Given fixed total investment size, it would be wise to just stick to Lump Sum.

The question remains. Is this true in general? Or does it have to do with the price trajectory of SPY in particular? I’ll answer this is the next post.

Investing Large Sum of Money: Part 1

In this series, I would like to try to answer a practical question I had in the past.

Let’s say you have access to a relatively large sum of cash in your hands available for investment. It may be year end cash bonus from your employer. It may be inheritance. Do you put every dollar into the stock on a single day? What if an unanticipated market correction begins just the next day?

Dollar cost averaging can help reduce the anxiety of having to time the market. However, depending on how much you spread out the investment, you can miss out on some good opportunities. How much are we missing out? Let’s see by using the history of SPY.

Below is the daily price of SPY in the past 25 years.

To evaluate the value of DCA, I’m going to do the following experiment. For each possible initial investment date, I’m going to compare the following two strategies: One, invest the entire amount on the initial date; Two, invest equal amount of money each day over the next year. Then I’m going to compare how much the aggregate investment have grown at the end of the year.

For example, let’s say I had $10,000 to invest on Jan 29, 1993 when the (adjusted) close price was at $27.235.

If I took the lump sum approach and purchased 367.1746 shares of SPY on Jan 29, 1993, my investment would have grown by 11.4% after a year. If I took the DCA approach and invested $10,000 / 252 = $39.68254 each day over the next year, I would be holding 350.4686 shares of SPY at the end of the year, which would be worth $10,633.

In the above example, DCA clearly lost by about 50%. It make sense. If you had dollar cost averaged into a savings account, you would have realized only half of the increase in value of lump sum savings account. So, we can expect that DCA approach would, on average, achieve about 50% of the return of the lump sum approach.

Below, I plotted out the scatterplot of the 1-year returns of the two strategies on every possible initial investment date since 1993.

We can verify from data that DCA on average achieves about half of the return of Lump Sum. Was DCA’s lower return justified by the risk? Below table answers the question.

mean std dev mean / std dev
LS 11.0% 17.2% 0.64
DCA 4.9% 9.4% 0.52

At least historically speaking, DCA has not been an attractive strategy to investing a large sum of money into SPY. Is there any other metrics I can look at? I’ll look at it in the next post.

Is the Stock Market Efficient?

As of July, 2018 I have about $170K invested in the stock market. About half of that is in a 401(k) account, and half in a brokerage account. As I began investing early in my career, I asked myself, do I want to invest in single stocks or in index funds? It was an easy choice for me. One, my employer made it pretty inconvenient to invest in stocks with approval processes, holding period limitations, and timing restrictions. Two, I didn’t have the money or the guts to invest large enough money to any individual stock to justify the brokerage commission (I’ll probably give Robinhood a shot if I do start investing in single stocks)Three, I just didn’t believe that I had done or could ever do enough research to beat the market.

My hesitation to invest in individual stocks evolved into more of a conviction after several years of professional experience in quantitative trading. Is the stock market efficient? NO. I have seen many groups of people consistently make lots of money in high and medium frequency space which contradicts EMH. However, that doesn’t mean that I have a meaningful shot at beating the market. I have personal experience only in the high/medium frequency space, but I can say that a lot of quantitative research goes into picking stocks in these firms. Beating the market is not as easy as it sounds in the media even for large trading firms. Competition is fierce and only the best survives in the long run. I can only assume the same goes for funds that trade in longer horizons.

If you trade relatively fast signals or news and hold a position for a short period of time (under a few months), it is almost guaranteed that some of the quantitative firms have already incorporated them into their models. They have much more resources to validate the alpha content of the information, are faster to trade, and are larger in size. Most of the time, you trade on alpha that has already been realized.

If you pick individual stocks and hold on to the positions for the long term, you would be doing so because you think your portfolio would do better than holding the broader market – say SPY. However, I do not believe that a typical individual can consistently beat the aggregate market, the majority of which are full time institutional investors with much more man power and better infrastructure than any individual. My belief is that the individual stocks are trading at fair value more often than not.

So it really depends on who you ask. The market is fairly efficient for most individuals. For competent traders with good enough infrastructure, it is far from it. They’re usually the ones that makes the market efficient. This is my rationale for investing in commission free low cost ETFs.

How do you approach investing? Do you pick your own stocks or do you invest in a passive fund? How do you go about timing? Share in the comments!


Net Worth Snapshot Jul 2018

  • I expected July to be a bad month because I had to take out a significant amount of money from my emergency fund. However, market had a good run earlier in the month which made up for the expense.
  • Other than the withdrawal from the emergency fund, a relatively quiet month with not much change overall.

I do have a lot of cash lying around. Most is earmarked for emergency fund, next year’s educational expense, etc. Most of cash is sitting in online savings accounts which are at around 1.75-1.85% annually. Any comments or advice about the current breakdown of my assets would be appreciated. Right now, cash/investment/home equity almost equally shares my net worth.


Catching Up with History

I have been keeping track of my household’s net worth on a spreadsheet for some time now. Before using a spreadsheet, I used Mint to keep track of my net worth, but after a friend of mine convinced me of the danger of keeping all my financial accounts in one location, I switched to manually updating the spreadsheet. It is more cumbersome to manually update the numbers, and I get lazy at times, but I found it helpful to force myself to mentally keep track of my net worth.

Above is the history of my net worth over the years with my current target of $1M at the top. I started to keep track of my net worth a bit after getting married. I only had a few years of experience back then and hadn’t accumulated much wealth. Below are some highlights since I started tracking.

  • My net worth has been increasing in a linear fashion, mostly due to year-end cash bonuses from my employer. I live in one of the priciest cities in the US and it’s been difficult to save up with only my base salary. It’s been even more difficult after the birth of my child.
  • I purchased my primary residence in the second half of 2014. The green line shows the equity I have built with my home. It is probably an underestimate as home prices have risen in the area since the purchase. I have only partially incorporated the rise in home price.
  • Blue line shows the sum of my brokerage accounts and 401(k). I’m mostly invested in index funds.

I’m already halfway to my target! However, there are some headwinds lying ahead. Expenses keep increasing as family grows (nannies, schools, etc.). My year-end bonuses are not guaranteed. I may change my career to a less lucrative field. The market is around its historical high.

Hopefully the trend will continue, and I’ll be able to adjust my target to a higher number in a few years. I will share monthly snapshots of my net worth starting with July 2018.

Follow my journey to $1 million and beyond!