# Determining the investment strategy

I have the following problem:

Consider the 5 year investment strategy and given the yearly portfolio returns $S_{t+1}/S_t$ and dividends $D_{t+1}$ paid at $t+1$ which are modeled as:

$\frac{S_{t+1}}{S_t}=e^{\mu+0.2X_{t+1}}$ and $\frac{D_{t+1}}{S_t}=0.05e^{-0.05^2/2+0.05Y_{t+1}}$ where both $X_i$'s and $Y_i$'s are independent and standard normally distributed.

The task is to determina a function $f$ for a investion of 1000000 dollars in a portfolio of stocks and reinsvesting the dividends in the portfolio of stocks such that the value of the portfolio in 5 years can be expressed as some function $V_5=f(\mu,X_i,Y_i)$ for $i=1,2,3,4,5$

I basically think this is just by using the given models for returns and dividends: $V_5 = 1000000e^{\mu+0.2X_{t+1}}+0.05e^{-0.05^2/2+0.05Y_{t+1}}$

However I am not sure if I have done this right? Any suggestions?

• You could improve the question title ... "function of a strategy" is quite unclear. – Ric Nov 9 '15 at 16:13
• If you are re-investing all the dividends in the same stock, then your strategy has already been determined. What you need is to find the value in 5 years. – Gordon Nov 9 '15 at 16:49
• Yes, I re-invest in the same portfolio of stocks. So my $V_5$ is correct? The next 5 years i can just simulate for each $t$ – Elekko Nov 9 '15 at 17:33
• Your question is not clear. What do you mean " determine a function $\cdots$ such that $\cdots$"? Is $V_5$ given? – Gordon Nov 9 '15 at 17:36
• $V_5$ is a "function" like $V_T = f(\mu, X_i, Y_i)$ that represents the whole strategy. For instance assume I own 1 stock of A and 2 stocks of B at time t=0. Then at time t=1, the portfolio is $V_1=S_{1}^A+2S_{1}^B$ – Elekko Nov 9 '15 at 17:46