Question

State of the market	Probability	Expected Return X	Expected Return Y
Boom	5%	+30%	+2%
Normal	15%	+3%	-5%
Recession	80%	-5%	-10%

1) IN the context of scenario analysis: what is expected return? What is Standard Deviation? How are they used to analyze possible securities?

2) Ca lulate the expdected return and standard deviation of stock X and stock Y.

Answer 1

1.

Scenario analysis refers to analysis of possible future events for example in above case, Boom, Normal & Recession are three scenario in future for the market.

In the context of scenario analysis - Expected Return {E(r)}

Expected Return E(r) is the weighted average of return of all possible scenario where weights are probability of scenario.

$E(r)=\sum_{i=1}^{n} R_{i}P_{i}$

where,

R = Expected Return in different scenario

P = Probability of different scenario

In the context of scenario analysis - Standard deviation ($\sigma$)

Standard deviation is a measure of deviation of return from Expected return E(r). In the context of scenario analysis, standard deviation weighted average of square of deviation where weights are probability of possible scenario.

$\sigma = \sum_{i=1}^{n}(R_{i}-E(r))^{2}*P_{i}$

Where

R = Return in different scenario

E(r) = Expected Return as explained above

P = Probability of different scenario

2.

Calculation of Expected Return and Standard deviation of Stock X and Stock Y

STOCK-X
State of the Market	Probability (P)	Return X (Rx)	(P*Rx)	D={Rx - E(rx)}^2	(D*P)
Boom	0.05	0.3	0.015	0.10272	0.00514
Normal	0.15	0.03	0.0045	0.00255	0.00038
Recession	0.80	-0.05	-0.04	0.00087	0.00070
Expected Return E(rx)			-0.0205	Standard deviation ($\sigma_{x}$)	0.00621
STOCK -Y
State of the Market	Probability (P)	Return Y (Ry)	(P*Ry)	D={Ry - E(ry)}^2	(D*P)
Boom	0.05	0.02	0.001	0.01134	0.00057
Normal	0.15	-0.05	-0.0075	0.00133	0.00020
Recession	0.80	-0.1	-0.08	0.00018	0.00015
Expected Return E(ry)			-0.0865	Standard deviation ($\sigma_{y}$)	0.00091

Please refer to below image for excel formula reference -

Formula reference -