Time-adjusted volatility and returns of equities and risk-free assets

Hello readers!

Some background

In this post we will be discussing about the impact of time in our portfolios. In many cases that you might have read or experienced, equities(or stocks) are deemed as a much riskier investment than fixed income assets, such as SGS (government) bonds, fixed deposit, or some guaranteed return savings plan offered by various insurance companies. The volatility is typically given by a few parameters, such as yearly standard deviation, maximum drawdown, variance, and so on. These volatility, or risk, are usually given in percentage values such as 20%, representing a chance that your investment might experience a 20% fall in net asset value.

Alongside that, we are also typically quoted a projected return, which is the amount that we should receive, on average, if there is nothing seriously wrong going on. There you have it, a classical risk-return picture painted for you by most financial advisers offering their products.

However, many ignore the fact that time heal all wounds (aha surprise, it's not only in your romance drama, it applies in finance as well). Historically, almost every crash will be followed up by a recovery. I use the word 'almost' because definitely you have some companies which are ousted by a crash, and have to declare bankruptcy and such, but this fact really does not apply to markets such as Dow Jones, STI, Hang Seng, and thus we can reasonably assume that a recovery will surely follow.

Let's get to the main point I am bringing across:

Holding riskier equities throughout a longer time horizon is overall more profitable than holding risk-free assets, even after taking risk into account.

Some caveats/assumptions before we proceed:

- Markets will recover fully to pre-crash values in 2 years

- Crash occurs in a 30% drop in NAV

- Crashes happens about ~7 years

Without much calculations, it is a given fact that equities tend to have a higher rate of return than risk-free assets. Of course, risk must and will be rewarded (if you know what you are doing).

Starting off at a base index of 100, I used a slightly random walk growth of the economy, based around the typical equities rate of return of 7%. Giving us something like this:

Yes, of course the natural thought is that no market is ever that stable, every now and then a recession will occur or in worse cases, a financial crisis of 2008. By accounting for random crashes every now and then (not too frequent of course, don't be so pessimistic man), we would get something like this, accounting for recovery as well :

Now we would get a graph that looks a bit more realistic, I would say not that far off from this:

At this point, we thus consider the difference of equities versus a risk-free asset such as bonds and saving plans. I will use a (slightly higher) rate than the bonds offered by SGS of 2.5% and endowment plans rate of 3.5% (if you actually know anyone offering similar products which has a higher guaranteed return feel free to tell me). Resulting comparison would look something like this :

As we can see, about 5 to 6 years in, a market crash might cause your net asset value (NAV) to be worse off than investing in SGS bonds or Endowment plans. In about 12 to 13 years in, an endowment plan might still fare better than equities, although from the graph it is clearly not significant, although it is safe all the way.

However, evidently, approaching the 20 year mark, a well-balanced equity portfolio that doesn't require astronomical risk/return would outperform any of the other 2 'risk-free' assets by a long shot. Even after a crash of 30% occurs, the NAV is no longer close to being lower than that of the risk-free assets.

Based on the very simple projections, one would approximately have:

3.65x of their capital if they invested in a balanced equity portfolio

1.63x of their capital if they invested in government bonds

1.99x of their capital if they invested in an savings/endowment plan.

Conclusion:

Based on your investment horizon, one should consider taking on more risky assets as the lost in opportunity costs would outweigh the safety net offered by risk-free assets given a time long enough.

Also, one should consider the uselessness of safety, in terms of low deviation and volatility, if their risk-free assets requires a long lock-in period, such as SGS bonds (10 years) or endowment plans (20 years), or if you really want a long one, CPF. Safety should come with liquidity, and if a guaranteed sum is not available for withdrawal purposes, then what is the use of it being risk-less?

Thanks for reading!

Feel free to hit me up for the excels, calculations, reasoning and further theory and assumptions if required. Credit me if you're gonna use my content anywhere. I also offer individual investments analyses and discussions for interested parties.