Question

You observe a portfolio for five years and determine that its average annual return is 13% and the standard deviation of its returns is 21%. Can you be 95% confident that this portfolio will not lose more than 30% of its value next year

Answer 1

Answer:

There is a 95% probability that the portfolio would not loose more than 30% of its value.

Step-by-step explanation:

The confidence interval for proportions (p) is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The information provided is:

$\hat p = 0.13\\\sqrt{\frac{\hat p(1-\hat p}{n}} =0.21$

For 95% confidence level the critical value of z is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

The 95% confidence interval for average annual return is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.13\pm 1.96\times0.21\\=0.13\pm 0.4116\\=(-0.2816, 0.5416)\\\approx(-28\%, 54\%)$

The lower limit of the 95% confidence interval is -28%.

This implies that the portfolio would not loose more than 28% of its value.

Thus, there is a 95% probability that the portfolio would not loose more than 30% of its value.