Hi all,
This is not necessarily a finance/business question, but i am wanting to use the equation in a finance setting so perhaps the question belongs here. I'm actually not sure what type of math is required or if the equation can even be solved.
Explanation
I have a situation where there are two entities, one is an investor, the other is a copycat. The copycat wants to replicate the investor's stock portfolio which consists of two factors 1) individual position weightings and 2) average price paid for individual positions.
If the copycat wants to simply mirror the individual position weightings its easy, he/she just needs to allocate the same value to each position, proportionate to the total portfolio value. However if the copycat is already holding individual positions where there average stock price paid is different from that of the investors, and they wish to correct (replicate) the average stock price paid for the individual positions with that of the investors, then we have the following problem;
How do I account for a variable delta when trying to replicate the average price of the investor?
There are a number of factors required to solve the equation:
Investor factors
a) Investor average price (the weighted average price of all buy prices weighted against all quantity of shares bought at that price)
b) Investor share quantity (the position value divided by the average price) c/a
c) Investor position value (the current stock price times the quantity of shares owned) k*b
d) Investor position weight (the position value divided by the total portfolio value) c/e
e) Investor portfolio value (the sum of all individual position values) sum-c
Copycat factors
f) Copycat average price
g) Copycat share quantity
h) Copycat position value
i) Copycat position weight
j) Copycat portfolio value
Equation factors
k) Current stock price [this factor is variable]
l) Delta as a percent (Investor portfolio weight minus Copycat portfolio weight) d-i [this factor is variable because the weights are determined by the position values which are determined by a variable stock price]
m) Delta as a value (Delta as a percent times Copycat portfolio value) i*e [this factor is also variable]
Other factors
n) Copycat's sum of future position value (copycats position value plus Delta as a value) h+m
o) Copycat future position weight (Copycat's sum of future position value divided by copycat portfolio value) n/j
p) Future delta as a percent (Copycat future position weight minus Investor position weight) o-d [this should equal 0% if the calculation is correct]
Solution
q) Correct stock buy price (for Copycat to buy at in order to mirror investors average price and position weight)
r) Correct share quantity to purchase (for Copycat to mirror investors average price and position weight) m/q
s) Copycat's new average price (mirrors Investors average price) s=a
Problems
How do i account for a variable delta? in the example provided (photo attached), if you were to assume the current stock price is $7.00, and the current delta is 4.67% (delta as a percent), and a delta in value of $2,333, and the stock price dropped from $7.00 to the correct stock price to buy of $3.69, the delta would then reduce and in turn the value to close would reduce, causing the correct stock buy price to change, therefore one factor required to solve the equation is the equation itself (Mutual recursion?) suggesting a higher form of math is required (algebra?)
Considerations
If the Copycat position weight is greater than the investors position weight, then the equation could not resolve to a positive number (i>d, ignore)
If the Copycat position weight is less than investors position weight, then what is the Correct stock buy price & Correct share quantity to purchase (i<d, solve q & r)
Clarification
See attached photo or visit this link where there is a spreadsheet. The spreadsheet Dashboard tab describes the final implementation style (pink border). The Helper tab (final columns on the right) outlay the relationship between the factors and example fictional data, the remainder of the spreadsheet is the actual data
If anyone knows if this equation is possible, and if so what type of math is required to resolve?
Much appreciated,
Stevo
This is not necessarily a finance/business question, but i am wanting to use the equation in a finance setting so perhaps the question belongs here. I'm actually not sure what type of math is required or if the equation can even be solved.
Explanation
I have a situation where there are two entities, one is an investor, the other is a copycat. The copycat wants to replicate the investor's stock portfolio which consists of two factors 1) individual position weightings and 2) average price paid for individual positions.
If the copycat wants to simply mirror the individual position weightings its easy, he/she just needs to allocate the same value to each position, proportionate to the total portfolio value. However if the copycat is already holding individual positions where there average stock price paid is different from that of the investors, and they wish to correct (replicate) the average stock price paid for the individual positions with that of the investors, then we have the following problem;
How do I account for a variable delta when trying to replicate the average price of the investor?
There are a number of factors required to solve the equation:
Investor factors
a) Investor average price (the weighted average price of all buy prices weighted against all quantity of shares bought at that price)
b) Investor share quantity (the position value divided by the average price) c/a
c) Investor position value (the current stock price times the quantity of shares owned) k*b
d) Investor position weight (the position value divided by the total portfolio value) c/e
e) Investor portfolio value (the sum of all individual position values) sum-c
Copycat factors
f) Copycat average price
g) Copycat share quantity
h) Copycat position value
i) Copycat position weight
j) Copycat portfolio value
Equation factors
k) Current stock price [this factor is variable]
l) Delta as a percent (Investor portfolio weight minus Copycat portfolio weight) d-i [this factor is variable because the weights are determined by the position values which are determined by a variable stock price]
m) Delta as a value (Delta as a percent times Copycat portfolio value) i*e [this factor is also variable]
Other factors
n) Copycat's sum of future position value (copycats position value plus Delta as a value) h+m
o) Copycat future position weight (Copycat's sum of future position value divided by copycat portfolio value) n/j
p) Future delta as a percent (Copycat future position weight minus Investor position weight) o-d [this should equal 0% if the calculation is correct]
Solution
q) Correct stock buy price (for Copycat to buy at in order to mirror investors average price and position weight)
r) Correct share quantity to purchase (for Copycat to mirror investors average price and position weight) m/q
s) Copycat's new average price (mirrors Investors average price) s=a
Problems
How do i account for a variable delta? in the example provided (photo attached), if you were to assume the current stock price is $7.00, and the current delta is 4.67% (delta as a percent), and a delta in value of $2,333, and the stock price dropped from $7.00 to the correct stock price to buy of $3.69, the delta would then reduce and in turn the value to close would reduce, causing the correct stock buy price to change, therefore one factor required to solve the equation is the equation itself (Mutual recursion?) suggesting a higher form of math is required (algebra?)
Considerations
If the Copycat position weight is greater than the investors position weight, then the equation could not resolve to a positive number (i>d, ignore)
If the Copycat position weight is less than investors position weight, then what is the Correct stock buy price & Correct share quantity to purchase (i<d, solve q & r)
Clarification
See attached photo or visit this link where there is a spreadsheet. The spreadsheet Dashboard tab describes the final implementation style (pink border). The Helper tab (final columns on the right) outlay the relationship between the factors and example fictional data, the remainder of the spreadsheet is the actual data
If anyone knows if this equation is possible, and if so what type of math is required to resolve?
Much appreciated,
Stevo
