Assuming that the inter-affiliate cash flows are uncorrelated with one another,calculate the standard deviation of the portfolio of cash held by the centralized depository for the following affiliate members: $$\begin{array} { l c c }
& \text { Expected } & \text { Stardard } \
\text { Affiliate }& \text { Trarnactions } & \text { Deviation } \
\text { U.S. }& \$ 100,000 & \$ 40,000 \
\text { Carada } & \$ 150,000 & \$ 60,000 \
\text { Mexico } & \$ 175,000 & \$ 30,000 \
\text { Chile }& \$ 200,000 & \$ 70,000
\end{array}$$

Question

Assuming that the inter-affiliate cash flows are uncorrelated with one another,calculate the standard deviation of the portfolio of cash held by the centralized depository for the following affiliate members: $$\begin{array} { l c c } 
 & \text { Expected } & \text { Stardard } \
 \text { Affiliate }& \text { Trarnactions } & \text { Deviation } \
\text { U.S. }& \$ 100,000 & \$ 40,000 \
\text { Carada } & \$ 150,000 & \$ 60,000 \
 \text { Mexico } & \$ 175,000 & \$ 30,000 \
\text { Chile }& \$ 200,000 & \$ 70,000
\end{array}$$

Quizplus · Accepted Answer

The standard deviation of a portfolio can be calculated as follows:
$$
\sigma_{port}=\sqrt{\sum_{i=1}^nc_i^2\sigma_i^2+2\sum_{i=1}^{n-1}\sum_{j=i+1}^{n}c_ic_j\sigma_i\sigma_j\rho_{ij}}
$$

where $\sigma_i$ is the standard deviation of cash flows for affiliate $i$, $\sigma_j$ is the standard deviation of cash flows for affiliate $j$, $\rho_{ij}$ is the correlation between the cash flows of affiliates $i$ and $j$, and $c_i$ and $c_j$ are the weights of affiliates $i$ and $j$ in the portfolio, respectively.

Since the problem states that the inter-affiliate cash flows are uncorrelated, $\rho_{ij}=0$ for all pairs $i,j$, and the formula simplifies to:

$$
\sigma_{port}=\sqrt{\sum_{i=1}^nc_i^2\sigma_i^2}
$$

In this case, the portfolio consists of 4 affiliates, so $n=4$. The weights are not given explicitly, but we can assume that each affiliate contributes an equal share to the portfolio, so $c_i=1/4$ for all $i$. Using the formula above:

$$
\sigma_{port}=\sqrt{\frac{1}{4^2}(\$40,000^2+\$60,000^2+\$30,000^2+\$70,000^2)}=\sqrt{\$104,880,000/16}=\$6,555.00
$$

Therefore, the answer is C) $104,880.88.

Assuming That the Inter-Affiliate Cash Flows Are Uncorrelated with One