CAPM essay

In the second scenario BBBY would use its $400 million in excess cash and borrow the remaining funds until
Question 2 a) We will need to calculate the debt-to GDP ratio for each year separately in order to compute the total accumulation.

The following equations and variables are used in question a)
∆b=g-t+r-y* b g-t=2 i=3 π=1 r=i-π=3-1=2 y=1 b=0,9 (=90%)
Year 1
∆b=2+2-1* 0,9=2,9 byear 1=90+2,9=92,9
Year 2
∆b=2+2-1* 0,929=2,929 byear 2=92,9+2,929=95,829
Year 3
∆b=2+2-1* 0,95829=2,95829 byear 3=95,829+2,95829=98,78729
Year 4
∆b=2+2-1* 0,9878729=2,9878729 byear 4=98,78729+2,9878729=101,7751629
Year 5
∆b=2+2-1* 1,017751629=3,017751629 byear 5=101,7751629+3,017751629=104,792914529
Therefore, after 5 years the debt-to-GDP ratio will be equal to 104,8 % (rounded to one decimal) b) The debt is not sustainable. The criteria to test whether debt is sustainable is as follows:
∆b=g-t+r-y* b=0
Plotting in the known variables results in the following:
∆b=2+2-1* b=2+b= 0

Solving for b gives the following: b= -2
Therefore, the initial debt should be -200% (so surplus) in order to maintain a sustainable debt. c) If the nominal interest rate rises to 10%, it would imply that the real interest rate is as follows:

r=i-π=10-π
Therefore, we know that:

∆b=g-t+r-y* b=2+10-π-1*0,9=2+9-π*0,9

The criteria to maintain a sustainable debt is as follows:
∆b=0
This implies that
∆b= 2+9-π*0,9=0 Solving for inflation results in the following: π ≈11,22
The conclusion is thus that debt in this scenario will only remain sustainable if the real rate of interest is negative (since the rate of inflation is higher that the nominal interest rate). d) I believe the question is rather whether both policies could cooperate, which according to me is not possible since fiscal policy is usually directed at increasing output and income whereas the primary goal of monetary policies is to maintain a low level of inflation. Therefore, both policies cannot cooperate.

* A dummy variable is a variable that takes on two values, usually 0 or 1. * I avoid here the notation N for sample size, which you know from your statistics course. There, N is reserved for population size. Usually the population size is not defined (we simple do not know it). In many economic publications N is used as the sample size. * What a histograms does is count the number of observations in certain intervals and display the result graphically * E(x) is the expected value (weighted average of all its values) or expectation of x The rth central moment is defined as: E(x−E(x))r,r=1,2,3,... They characterize populations or population distributions. * First moment Population mean (r = 1: E(x1)=E(x)) [Do not confuse with first central moment, which is always one (=1)] * Second central moment Variance E(x−E(x))2 * Third central moment Related to skewness of distribution * Positively skewed = Tail extending to right * Negatively skewed = Tail extending to left * Fourth central moment Related to the kurtosis (= any measure for peakedness for the distribution of a real random variable) * If we multiply each xi in a series with k , then you can also multiply the total summation of xi with k * E(x)=∑all possible x x⋅P( x) [=population mean/first moment of discrete random variables/mean] * E(g(x))≠g( E(x)) [This only holds when g(x) is a linear function] * The continuous variable z can take an indefinite (uncountable) number of different values, therefore P(z) = 0. Hence, we have to rely on a density function. * The following requirements apply to a probability density function f(x) whose range is a ≤ x ≤ b. * f(x) ≥ 0 for all x between a and b * The total area under the curve between a and b is 1.0 * Vertical axis of probability density function = density * Density = Frequency/Class width (Just like a histogram) * The area under the probability density function corresponds to probability, not the vertical axis! * Expected value of continuous variable:

* The expectation of a function, day g(z)