Pricing a portfolio

[Jagra]

Hi everybody,

I need to price a portfolio, but I have some specific kinds of data to input and a specific format to output and I can't quite figure out how to do it.

Inputs: I have price relatives for a number of stocks. Price relatives differ from percent changes in that the 1st price in a series represents 1 or 100% of the position in that stock. If after some amount of time the stock increased by 10% from the start, the price relative would equal 1.1. If it had fallen 10% from its start it would equal 0.9.

Let the following represent the price relatives at a single time interval for n stocks:

Stocks = {S1, S2, S3, S4, ..., Sn}
​

I also have corresponding, weights which define the allocation for each of the stocks in a given portfolio:

Allocations = {A1, A2, A3, A4, ..., An}
​

The allocations in a basic portfolio with neither leverage or shorts must equal 1 (100% of the portfolio).

Some data to illustrate:

Stocks = {1.0190, 1.0383. 0.9982, 1,.0128, 1.0133, 0.9963, 0.9999, 1.0248}
Allocations = {0.02500, .39000, .21000, .04000, .30000, .00500, .00100, .02900}

Also, the value of the portfolio of stocks with any given corresponding allocations at time period 1 must equal 1 (100% of the portfolio).

Now I get confused. How do I calculate the value of the portfolio?

The first thing to consider would be this:

(S1 * A1 + S2 * A2 + S3 * A3 + S4 * A4 ... + Sn * An)

But I don't think that will work for leveraged or short allocations. So I thought I would need to do something like this:

1 +((S1 - 1) * A1 + (S2 - 1) * A2 + (S3 - 1) * A3 + (S4 - 1) * A4 ... + (Sn - 1) * An)

But I'm not certain.

Someone suggested something like this (without explanation):

1 + ((S1 * A1 * S2 * A2 * S3 * A3 * S4 * A4 ... * Sn * An)^(1/n))

So I need and approach to price portfolios given current price relatives and allocation weights that will work with long only portfolios, leveraged, and short portfolios.

If anyone has a solution, suggestion, or guidance I'd really appreciate it.

Thx.

 

[aaps]

I got confused when I looked at the example you put:
Stocks = {1.0190, 1.0383. 0.9982, 1,.0128, 1.0133, 0.9963, 0.9999, 1.0248}

Is that the return of each stock in time t + 1? If this is the case, then you should instead work with
Stocks = {0.0190, 0.0383. -0.0018...}

Then you just have to compute the inner product of your vector of weights (allocations) by the vector of returns. It doesn't matter of you have long and short positions; this should be appropriately reflected in your vector of weights. (Short positions have a negative weight and long positions a positive weight; they still have to sum up to 1 if this is a self financed portfolio.)