QUESTION $5($RISK AND RETURN$)$

$(22$ MARKS$)$

Evashin $($Pty$)$ Ltd has the following analysis of past returns and forecast has been carried out and it offers the probability distribution of returns on different given states of the economy:

$\backslash$table$[[$State of the Economy,Probability of State of the Economy,Return$($Ri$)],[$Super boom,$10\%,50\%],[$Boom$,30\%,30\%],[$Normal$,50\%,10\%],[$Recession$,15\%,-10\%],[$Severe recession,$10\%,-20\%]]$

Required

Calculate the following based on the different probabilities of the stages of the economy.

$($i$)$ average expected return

$[3]$

$($ii$)$ variance

$[5]$

$($iii$)$ standard deviation

$[5]$

The following formulas should be used. Round off to $2$ decimal places

$Re={\displaystyle \underset{im1}{\overset{?}{}}}(Ri)$

Numen$-10x$ xomen

Use the format below for the calculation of the above.

Draw the following template in your answer booklet provided.

$\backslash$table$[[\backslash$table$[[$State of$],[$Economy$]],\backslash$table$[[$Probability$],[$of state$],[($P$)]],\backslash$table$[[$Return$],[($R$)]],\backslash$table$[[$PXR of$],[$the$],[$economy$]],$cdots,${\displaystyle \underset{?}{\overset{?}{}}}P(R-Re{)}^2$