• Arpit Agrawal

The Idea of Passive Investment

Like most people around me, I grew up believing investing in stocks was no different from gambling and that timing is key to making money here. I was, however, relieved when I came across passive investment, a technique that does not require one to time the market and is well-founded in statistics. Before I talk about passive investment though, I want to describe what investment means more generally.

One who consumes less than they earn is a net saver; people tend to be net savers in good times to allow room for consumption in times of less income. When you save money, someone with a net deficit could put this money to better use: a start-up or corporate raising funds or an individual buying a car or building their house. Since you are parting with your money by withholding your consumption, you get rewarded in the form of interest or a share of profit above your initial amount at the end of the transaction. In short, investment is putting your unused money to work for you in return for a fixed or proportional reward.

Bonds and Stocks

In conventional investment theory, we have two classes of investments: bonds (this includes your checking and saving accounts in the bank) and stocks. There are other investments like real estate or commodities like gold, but we ignore them for simplicity. While the payoff of investing in bonds is deterministic (called interest), the payoff coming from stocks is stochastic (i.e. has a probability distribution instead of taking a fixed value). Anyone who is not a compulsive gambler would prefer to get money deterministically to stochastically if they were to get the same amount. Hence investing in stocks only makes sense if they offer a higher return in expectation. This extra expected return one gets from stocks is known as equity risk premium and is a key factor in deciding how you divide your money between bonds and stocks.

Understanding Stochastic Returns

It is common to link investing in stocks to gambling because both let you lose money with some probability. However, if you were to buy a large number of lottery tickets, it is likely you would lose more money in the price of the tickets than you would make from winning some of them. On the other hand, if you invest in a lot of stocks over a very long period, you make money because you are investing in a company that is expected to generate value “on average”. This average return is hard to see because the actual returns differ from the average a lot, sometimes on the higher and sometimes on the lower side (thus averaging to the average value). This variance (a measure of the distance of individual observations from the average) is often termed as risk and risky security is only worthy of investment if it offers a higher average return (risk premium).

The Averaging Effect

It is useful to know from statistics that the average of a large number of independent stochastic variables has lower variance than each of them. For example, remember how you would average your readings from a physics experiment in school to reduce variance. This way, even if a couple of readings were off-expectations, you could still get the right results. Similarly, in the context of investment, you can lower the variance in your returns by investing in a large number of unrelated stocks instead of just one stock. In practice, this does not eliminate all the variance since most stocks are positively correlated with the general health of the economy and are thus not independent of each other. Unless having too many stocks in your portfolio causes you trouble managing them or you have a good reason to exclude some stocks, you would always prefer a more diversified portfolio than a less diversified one.

Further, if you were to hold your portfolio of stocks for a longer duration (say 10 years as opposed to just one year), your average annual return would be closer to the expected return. This allows you to invest more money in stocks (versus bonds) when investing for a longer duration.


When you hold your investments for a longer duration of time, you benefit not just from averaging of returns but also a phenomenon often termed as compounding. In simpler terms, when a fixed amount of money is invested such that the return in each unit of time is proportional to the amount invested, your money grows exponentially instead of linearly. This happens because, at every unit of time, you don’t just earn interest on what you invested initially but also on the interest you have accumulated over time. This effect gets stronger as the investment is held for longer, which is why one should start investing as early as possible. As seen in the plots below, $1 invested at 4% per annum grows almost linearly for the first ten years, while it is hard to miss the exponential growth over 60 years.

Picking stocks is hard

You can make money by actively picking stocks if you can accurately price the stocks and find the ones trading below their share price and buy them (or short* the ones trading above the share price if you have the access). However, both these conditions are hard to achieve. First, pricing a stock accurately is difficult since that requires accurate forecasts of the cash flows of the company it represents along with the uncertainty of these cash flows. Further, companies often trade close to the fair price since most market participants price it in similar ways. The only way you could make money by this exercise (in a systematic way, that is) is by either having information that other people do not have (trading on which may be illegal depending on the source of the information) or being significantly smarter than everyone else to price the stock better than everyone. In theory, both situations are possible but very improbable.

What is a passive investment?

Passive investment is a strategy where instead of actively choosing bonds and stocks best suited for you, you invest in a well-diversified portfolio of bonds and stocks based on a fixed set of rules. You first decide your risk appetite to decide the proportion you would invest in stocks vs bonds and then use that proportion to invest in well-diversified portfolios of bonds and stocks each. The risk appetite depends among other things on the duration you are saving your money for, the stability of your income, the liabilities you can foresee, and how well you understand the financial markets. For the second step in most developed markets, it is easy to find low-cost products that help you invest in such bond and stock portfolios (often called index funds). Over time as the date of redeeming your savings comes closer, you may gradually move your money from stocks to bonds. Thus you make very few transactions (say a couple of transactions per month) and also make very few active decisions.

Why go passive?

By investing money passively, the first obvious saving you make is in the commissions or transaction fee that you pay to your broker/exchange. Further, in some jurisdictions, you may get favorable tax treatment if you hold securities for longer. I feel that the biggest upside is in the time saved by not closely following news that can potentially impact your investments in the short-run.

Is it always the way to go?

The basic tenet on which passive investment works is that it is hard for one to beat the market without significant effort. However, if you are an investor with access to some opportunities that others cannot access (for example an employee discount on some shares), you might get superior returns from such investments. Also while it is hard to pick the right stocks, it is not impossible.

Generalizing to other asset classes

While I have mostly talked about bonds and stocks in this post, the general ideas work well for any asset classes you might want to invest in.

  • You should start investing as early as possible to benefit from compounding returns

  • You can invest in riskier assets if you are investing for a longer period of time

  • You can diversify your risk by investing in a bigger number of unrelated risky assets rather than concentrating risk in one big risky asset

To get more details into a passive investment, I'd recommend the Boggleheads wiki, and also the subreddit r/personalfinance for planning your personal finances.

* Short-selling is when you sell a share even without owning it. One typically does this by borrowing the shares from someone who already owns them. You can also be ‘short’ in a stock (i.e. benefit from the stock price going down) by trading derivatives such as futures and options.
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