Economic Investment Quantity
Francois
formula: EOQ = SQRT( ( 2 x Co x D ) / Ch )
where
Co = Cost to place one order for stock
D = Annual demand for stock
Ch = Variable cost associated with holding one item of stock in
inventory
Bauman suggest this formula can be used to manage cash transactions,
as follows:
formula: EOQ = SQRT( ( 2 x Co x D ) / i )
where
Co = transaction cost for cash transactions
D = annual demand for cash in the business
i = annual interest rate
Therefore, can the EOQ formula be used to determine the optimum amount
of money to invest at any time, asuming that regular fixed investments
are made, as follow:
formula: EIQ = SQRT( ( 2 x Co x D ) / R )
where
Co = transaction cost to purchase shares
D = total annual amount available to invest
r = expected annual return on the investment
Do anyone know if the EOQ has been used this way before and if so,
then
what is the name of the formula?
( I am calling it the Economic Investment Quantity )
Thanks !
Francois
Verismall Software
www.verismall.com
John Bailey
wrote:
>Based on the Economic Order Quantity model:
>Therefore, can the EOQ formula be used to determine the optimum amount
>of money to invest at any time, asuming that regular fixed investments
>are made, as follow:
>
>formula: EIQ = SQRT( ( 2 x Co x D ) / R )
>where
>Co = transaction cost to purchase shares
>D = total annual amount available to invest
>r = expected annual return on the investment
Interesting. It would make a nice student paper to compare the
underlying assumptions of this approach--which may favor liquidity and
the Kelly Fraction approach,
http://home.rochester.rr.com/jbxroads/kelly/
which favors avoiding going broke. At a quick glance, the two methods
would not yield the same answer. Two optimizations cannot both be
right...unless their optimization bases were somehow different.
Kelly betting is a concept developed at Bell Labs as an offshoot of
Shannon's information theory and more recently applied to gambling
situations such as blackjack. My jbxroads/kelly article applies Kelly
Betting to investment portfolios. In Kelly betting, the amount
wagered is scaled to the odds. At even odds, bet nothing. The amount
to bet is called the Kelly fraction. If used, the theory claims the
amount won will grow exponentially. Applied to investment quantity, a
set of graphs with market growth and volatility determines the
investment fraction.
John Bailey
http://home.rochester.rr.com/jbxroads/mailto.html
Francois
> Based on the Economic Order Quantity model:
>
> where
> Co = transaction cost to purchase shares
> D = total annual amount available to invest
> r = expected annual return on the investment
>
Suggest the following variation of the formula above:
EIQ = SQRT( ( 2 x Co x D ) / R )
where
Co = transaction cost to invest the money
D = total amount of money available to invest
R = required return by investor(s) / borowing cost (interest rate) /
weighted cost of capital
Assumptions:
1. There is a financing cost for using the money for investment, i.e.
interest rate for money borrowed or weighted cost of capital if using
company funds.
2. Regular investments can be made throughout the year.
3. Financing cost (R) is incurred only once money is invested.
(important)
I've tested this formula with a manual calculation by comparing total
costs for regular investments using the EIQ against an initial lump
sum investment method. The EIQ reduces costs by mainly limiting the R
component of the formula.
Francois Terblanche
Verismall Software
www.verismall.com