Question

On February IN , Marshak's investment account has a balance Of $19,800. He deposited ,200 on April I and $2,600 on May l . He withdrew $8,400 on July l. On November I , Arshak's balance was $14,820. Find Arshak's approximate dollar-weighted annual yield for this nine-month period using (2.6.5).

Answer 1

The dollar-weighted annual yield for this nine-month period is -2.7%.

Solution:

The investment of deposit on April 1 (Feb, March = 2 months)

$\Rightarrow\frac{(9-2)}{9}\times1200=\frac{(7)}{9}\times1200$

The investment of deposit on May 1 (Feb, March, April = 3 months)

$\Rightarrow\frac{(9-3)}{9}\times1200=\frac{(6)}{9}\times1200$

Therefore, Dollar-weighted annual yield for this nine-month period,

$\Rightarrow \frac{\text{Total interest}}{\text{Total investments}}$

On plugging-in the values,

$\Rightarrow\frac{14820-(19800+1200+2600-8400}{19800+\frac{7}{9}(1200)+\frac{6}{9}(2600)-8400}=-0.027$

In percentage notation,

$-0.027=(-0.027\times100)\frac{1}{100}=-2.7\% (\because \frac{1}{100}=\%)$