Question
(a) A stock has the following predicted returns under the following economic conditions:
Economic Condition Probability Return (K)
Recession 0.30 50
Stable economy 0.3 100
Moderate growth 0.3 120
Boom 0.10 200
Clearly and Step by step Compute the following
(i) Expected monetary value.
(ii) Standard deviation.
(iii)Coefficient of variation.
(iv)Return-to-risk ratio.
(b) The following are the average daily wages in kwachas of a group of industrial workers and
price indices:
Year 1999 2000 2001 2002 2003 2004
Daily Wages 80 108 125 147 216 230
Consumer Price 100 120 125 140 180 200
(a) Clearly and step by step Calculate the Real Wages, Money Wage Index and Real Wage Index
(b) Clearly and step by step Calculate the purchasing power of kwacha for the year 2004 as compared to the year 1999.
What is the significance of this result?
(c) How much is the worth of one kwacha of 1999 in 2003?
(d) In which year did the workers have the greatest buying power?
(e) What percentage increase in daily wages for the year 1999 is required (if any) to provide
the same buying power that the workers enjoyed in the year in which they had the greatest
buying power?
Economic Condition Probability Return (K)
Recession 0.30 50
Stable economy 0.3 100
Moderate growth 0.3 120
Boom 0.10 200
Clearly and Step by step Compute the following
(i) Expected monetary value.
(ii) Standard deviation.
(iii)Coefficient of variation.
(iv)Return-to-risk ratio.
(b) The following are the average daily wages in kwachas of a group of industrial workers and
price indices:
Year 1999 2000 2001 2002 2003 2004
Daily Wages 80 108 125 147 216 230
Consumer Price 100 120 125 140 180 200
(a) Clearly and step by step Calculate the Real Wages, Money Wage Index and Real Wage Index
(b) Clearly and step by step Calculate the purchasing power of kwacha for the year 2004 as compared to the year 1999.
What is the significance of this result?
(c) How much is the worth of one kwacha of 1999 in 2003?
(d) In which year did the workers have the greatest buying power?
(e) What percentage increase in daily wages for the year 1999 is required (if any) to provide
the same buying power that the workers enjoyed in the year in which they had the greatest
buying power?
Answers
GPT 3.5
(a)
(i) Expected monetary value (EMV) = Σ(Probability * Return)
EMV = (0.30 * 50) + (0.3 * 100) + (0.3 * 120) + (0.10 * 200)
EMV = 15 + 30 + 36 + 20
EMV = 101
(ii) Standard deviation = sqrt[Σ(Probability * (Return - Expected Return)^2)]
Standard deviation = sqrt[(0.30*(50-101)^2) + (0.3*(100-101)^2) + (0.3*(120-101)^2) + (0.10*(200-101)^2)]
Standard deviation = sqrt[(0.30 * 2601) + (0.3 * 1) + (0.3 * 361) + (0.10 * 9801)]
Standard deviation = sqrt[780.3 + 0.3 + 108.3 + 980.1]
Standard deviation = sqrt(1868)
Standard deviation = 43.24
(iii) Coefficient of variation = (Standard deviation / Expected value) * 100
Coefficient of variation = (43.24 / 101) * 100
Coefficient of variation = 42.82%
(iv)Return-to-risk ratio = Expected return / Standard deviation
Return-to-risk ratio = 101 / 43.24
Return-to-risk ratio = 2.34
(b)
Real Wages = Daily Wages / Consumer Price Index * 100
Money Wage Index = (Daily Wages in a particular year / Daily Wages in 1999) * 100
Real Wage Index = Money Wage Index / Consumer Price Index * 100
For each year:
1999:
Real Wages = 80/100 * 100 = 80
Money Wage Index = (80/80) * 100 = 100
Real Wage Index = 100/100 * 100 = 100
2004:
Real Wages = 230/200 * 100 = 115
Money Wage Index = (230/80) * 100 = 287.5
Real Wage Index = 287.5/200 * 100 = 143.75
(c) To find the worth of 1 kwacha in 2003 compared to 1999:
1 kwacha in 1999 is worth 1 kwacha
1 kwacha in 2003 is worth 140/100 = 1.4 kwachas in 1999
(d) The workers had the greatest buying power in 2004.
(e) Percentage increase required in daily wages for the year 1999 to provide the same buying power as in 2004:
(Required increase) = ((Real Wage Index in 2004) / (Real Wage Index in 1999)) * 100
Required increase = (143.75/100) * 100
Required increase = 43.75%
(i) Expected monetary value (EMV) = Σ(Probability * Return)
EMV = (0.30 * 50) + (0.3 * 100) + (0.3 * 120) + (0.10 * 200)
EMV = 15 + 30 + 36 + 20
EMV = 101
(ii) Standard deviation = sqrt[Σ(Probability * (Return - Expected Return)^2)]
Standard deviation = sqrt[(0.30*(50-101)^2) + (0.3*(100-101)^2) + (0.3*(120-101)^2) + (0.10*(200-101)^2)]
Standard deviation = sqrt[(0.30 * 2601) + (0.3 * 1) + (0.3 * 361) + (0.10 * 9801)]
Standard deviation = sqrt[780.3 + 0.3 + 108.3 + 980.1]
Standard deviation = sqrt(1868)
Standard deviation = 43.24
(iii) Coefficient of variation = (Standard deviation / Expected value) * 100
Coefficient of variation = (43.24 / 101) * 100
Coefficient of variation = 42.82%
(iv)Return-to-risk ratio = Expected return / Standard deviation
Return-to-risk ratio = 101 / 43.24
Return-to-risk ratio = 2.34
(b)
Real Wages = Daily Wages / Consumer Price Index * 100
Money Wage Index = (Daily Wages in a particular year / Daily Wages in 1999) * 100
Real Wage Index = Money Wage Index / Consumer Price Index * 100
For each year:
1999:
Real Wages = 80/100 * 100 = 80
Money Wage Index = (80/80) * 100 = 100
Real Wage Index = 100/100 * 100 = 100
2004:
Real Wages = 230/200 * 100 = 115
Money Wage Index = (230/80) * 100 = 287.5
Real Wage Index = 287.5/200 * 100 = 143.75
(c) To find the worth of 1 kwacha in 2003 compared to 1999:
1 kwacha in 1999 is worth 1 kwacha
1 kwacha in 2003 is worth 140/100 = 1.4 kwachas in 1999
(d) The workers had the greatest buying power in 2004.
(e) Percentage increase required in daily wages for the year 1999 to provide the same buying power as in 2004:
(Required increase) = ((Real Wage Index in 2004) / (Real Wage Index in 1999)) * 100
Required increase = (143.75/100) * 100
Required increase = 43.75%