Question

Buy-side vs. sell-side analysts’ earnings forecasts. Financial analysts who make forecasts of stock prices are categorized as either “buy-side” analysts or “sell-side” analysts. Refer to the Financial Analysts Journal (July/August 2008) comparison of earnings forecasts of buy-side and sell-side analysts, Exercise 2.86 (p. 112). The mean and standard deviation of forecast errors for both types of analysts are reproduced in the table. Assume that the distribution of forecast errors are approximately normally distributed.

a. Find the probability that a buy-side analyst has a forecast error of +2.00 or higher.

b. Find the probability that a sell-side analyst has a forecast error of +2.00 or higher

	Buy-Side Analysts	Sell-Side Analysts
Mean	0.85	-0.05
Standard Deviation	1.93	0.85

Short answer

a. Theprobability that a buy-side analyst has a forecast error of +2.00 or higher is0.2743.

b. Theprobability that a sell-side analyst has a forecast error of +2.00 or higher is0.008.

Step-by-step solution

Given information

Regarding exercise 2.86,the distribution of forecast errors from buy-side analysts follows a normal distribution with a mean of 0.85 and a standard deviation of 1.93. The distribution of forecast errors from sell-side analysts follows a normal distribution with a mean of -0.05 and a standard deviation of 0.85.

Step 2:(a) Calculate the probability

$x ~ N\left(\mu ,{\sigma }^2\right)$where$\mu =0.85 and \sigma =1.93$

$x=2$

The z-score is,

$\begin{array}{rcl}z& =& \frac{x-\mu }{\sigma }\\ & =& \frac{2-0.85}{1.93}\\ & =& 0.595855\\ & \approx & 0.6\\ & & \end{array}$

$\begin{array}{rcl}P\left(x⩾2\right)& =& \left(1-P\left(x<2\right)\right)\\ & =& \left(1-P\left(z<0.6\right)\right)\\ & =& 1-0.7257\\ & =& 0.2743\\ & & \end{array}$

$P\left(x⩾2\right)=0.2743$

Therefore, the probability that a buy-side analyst has a forecast error of +2.00 or higher is0.2743.

Step 3:(b) Calculate the probability

$x ~ N\left(\mu ,{\sigma }^2\right)$where$\mu =-0.05 and \sigma =0.85$

$x=2$

The z-score is,

$\begin{array}{rcl}z& =& \frac{x-\mu }{\sigma }\\ & =& \frac{2-\left(-0.05\right)}{0.85}\\ & =& \frac{2.05}{0.85}\\ & =& 2.411765\\ & \approx & 2.41\\ & & \end{array}$

$\begin{array}{rcl}P\left(x⩾2\right)& =& \left(1-P\left(x<2\right)\right)\\ & =& \left(1-P\left(z<2.41\right)\right)\\ & =& 1-0.9920\\ & =& 0.008\\ & & \end{array}$

$P\left(x⩾2\right)=0.008$

Therefore, the probability that a sell-side analyst has a forecast error of +2.00 or higher is 0.008.