Sunday, August 16, 2020

Maths: On maintaining or increasing dollar cost average

Have taken a short hiatus since my last post. With the February March crash well and truly behind us, the last two months in the market have been extremely flat. Long gone are the days of extreme volatility and since mid June, not much has really happened. This is clearly evidenced in the below chart:




As I write this, the ASX stands at 6126 points, a good 15% below the all time high of 7199. Although the S&P 500 has since reached all time highs and NASDAQ has long surpassed it, the ASX remains steady at around the 6000 to 6100 mark.

Given what had happened in February and March, ボーイフレンド had been a strong advocate for investing more and more the greater the deviation from all time high. At the bottom of the market, he was putting in 16 times his usual investment amount on a monthly basis, and then gradually scaling back as the market recovered. Where we are now, he is still putting in 4 times the usual, which has obviously impacted on cash reserves. With my limited resources, I am also putting in double what I would normally invest into the market. This has obviously resulted in fairly good returns for the both of us, he has long recouped all losses whereas I am roughly breaking even, even though the local market is still significantly lower than it was.

This brings me to current day, where we have fluctuated around this mark for about two months and I had been pondering whether or not to reduce our contributions given it had been eating into our cash reserves and that some developed countries had opted to go into lockdown again given second wave covid.

Essentially the dilemma I was facing was as follows:

  • If I keep contributing a greater amount than usual and the market crashes or suffers a correction due to second round lockdowns or other unforeseen circumstances, the funds I had invested in the market would be hit and I would also have a significantly lower cash reserve to throw into the market to get the benefit of better value shares.
  • If I reduced my contribution to my original standard amount, even though the market stands at 15% lower than all time high, and a crash does not occur, the cash I hold in the bank will be making negligible returns and whatever I do not invest now will have to be invested at a later date where the prices may have inflated considerably.
In pondering what to do with this conundrum, he mentioned the utility in working it out via outcome matrix given the range of potential situations and our three variables:
  • Increased or standard contribution
  • Depth of crash
  • Potential of crash
We worked this out using the following simulation. Whilst the current Australian CAPE stands at 19, there was no consideration for us to cash out any of our holdings, which meant at least one less factor. Assumptions we made in the following examples are as follows:
  • Standard contribution is $5,000 per month, increased contribution is $10,000 per month
  • Where the market doesn't crash, it goes up by the annual amount of 10%
  • Starting portfolio is $0 as what is already in the market is irrelevant.
Outcomes of our simulations are as follows:

Allowing for a 40% crash in 3 months



Allowing for a 30% crash in 3 months



Allowing for a 20% crash in 3 months




From the results, it can be easily distilled that the lower the chance of a crash, the better it is to go in with a higher contribution so as to maximize returns on cash. By putting these numbers into the matrices provides a quantifiable outcome for either scenario, thereby allowing me to consider which course of action I ought to take.

With the Australian Market pricing in zero profits across the board for the future year and a half (using CAPM and DCF models given risk free rates), it is fairly safe to say that the odds of a significant correction in the market is lower than usual, provided a Republican win in the Presidential Election in USA. Given the above modelling definitively shows that there is a strong reason to continue to contribute aggressively to the market whilst prices are still at their current rates.

by 小福