I can only afford to invest around HKD $12000 (USD $1500 ) each month, but the brokeage minimum charge is approx HKD $31 (currency exchange + commsion), which accounts for 0.25% of my investment. That seems like a lot to me, so I wondered whether I should invest every 2 months, or every quarter? If I wait too long, I loose time in the market. So what's the optimal # of months I should save and invest?
I came across this Taiwanese article, created a formula to calculate this.
https://yp-finance.com/optimal-investme ... 3a1hWDxa7k
Assuming the transaction minimum charge is 'c', the monthly investment amount is 'm' for every 'x' months, and the expected monthly return is 'r', calculated using simple interest, we can derive the following formulas:
Transaction minimum charge = c
Opportunity cost = ((x-1) + (x-2) + … + 1)mr + 0 = mxr * (x-1) / 2
To determine the most cost-effective investment interval, we need to calculate the minimum cost per unit investment.
Cost per unit investment = (Transaction minimum charge + Loss of unrealized returns) / Total cost
Cost per unit investment = (c + ((x-1)/2) * rmx)) / mx = c / mx + rx / 2 — r / 2
In this formula, we can ignore the last constant term, which means we only need to find the minimum value of:
Minimum cost per unit = c / mx + rx / 2
Based on the concept that the arithmetic mean > geometric mean, c / mx = rx / 2 will yield the minimum value. Therefore, to determine the investment interval 'x' in months, we can calculate the following formula:
Optimal waiting time (months) = sqrt(2*c / mr)
Optimal waiting time (months) = sqrt(2 * transaction minimum charge / (monthly return rate * monthly investment amount))
___
According to this formula, if I assume investment return is 6% annually (eqivalent to 0.49% monthly return), my best bet is to invest every month since:
sqrt(2 * 31 / (0.0049 * 12000)) = 1.02
Do you think this formula is sound?
I came across this Taiwanese article, created a formula to calculate this.
https://yp-finance.com/optimal-investme ... 3a1hWDxa7k
Assuming the transaction minimum charge is 'c', the monthly investment amount is 'm' for every 'x' months, and the expected monthly return is 'r', calculated using simple interest, we can derive the following formulas:
Transaction minimum charge = c
Opportunity cost = ((x-1) + (x-2) + … + 1)mr + 0 = mxr * (x-1) / 2
To determine the most cost-effective investment interval, we need to calculate the minimum cost per unit investment.
Cost per unit investment = (Transaction minimum charge + Loss of unrealized returns) / Total cost
Cost per unit investment = (c + ((x-1)/2) * rmx)) / mx = c / mx + rx / 2 — r / 2
In this formula, we can ignore the last constant term, which means we only need to find the minimum value of:
Minimum cost per unit = c / mx + rx / 2
Based on the concept that the arithmetic mean > geometric mean, c / mx = rx / 2 will yield the minimum value. Therefore, to determine the investment interval 'x' in months, we can calculate the following formula:
Optimal waiting time (months) = sqrt(2*c / mr)
Optimal waiting time (months) = sqrt(2 * transaction minimum charge / (monthly return rate * monthly investment amount))
___
According to this formula, if I assume investment return is 6% annually (eqivalent to 0.49% monthly return), my best bet is to invest every month since:
sqrt(2 * 31 / (0.0049 * 12000)) = 1.02
Do you think this formula is sound?
Statistics: Posted by phpwind0 — Sat Apr 06, 2024 3:12 am — Replies 0 — Views 22