DECLINING NUMBER OF PAY PHONES As cell phones proliferate, the number of pay phones continues to drop. The number of pay phones from 2004 through 2009 (in millions) are shown in the following table ( x = 0 corresponds to 2004 ): Year, x 0 1 2 3 4 5 Number of Pay Phones, y 1.30 1.15 1.00 0.84 0.69 0.56 a. Plot the number of pay phones ( y ) versus the year ( x ) . b. Draw the straight line L through the points ( 0 , 1.30 ) and ( 5 , 0.56 ) . c. Derive an equation for the line L . d. Using the equation in part ( c ) , estimate the number of pay phones in 2012 .
DECLINING NUMBER OF PAY PHONES As cell phones proliferate, the number of pay phones continues to drop. The number of pay phones from 2004 through 2009 (in millions) are shown in the following table ( x = 0 corresponds to 2004 ): Year, x 0 1 2 3 4 5 Number of Pay Phones, y 1.30 1.15 1.00 0.84 0.69 0.56 a. Plot the number of pay phones ( y ) versus the year ( x ) . b. Draw the straight line L through the points ( 0 , 1.30 ) and ( 5 , 0.56 ) . c. Derive an equation for the line L . d. Using the equation in part ( c ) , estimate the number of pay phones in 2012 .
DECLINING NUMBER OF PAY PHONES As cell phones proliferate, the number of pay phones continues to drop. The number of pay phones from
2004
through
2009
(in millions) are shown in the following table (
x
=
0
corresponds to
2004
):
Year,x
0
1
2
3
4
5
Number of Pay Phones, y
1.30
1.15
1.00
0.84
0.69
0.56
a. Plot the number of pay phones
(
y
)
versus the year
(
x
)
.
b. Draw the straight line
L
through the points
(
0
,
1.30
)
and
(
5
,
0.56
)
.
c. Derive an equation for the line
L
.
d. Using the equation in part
(
c
)
, estimate the number of pay phones in
2012
.
1 (Expected Shortfall)
Suppose the price of an asset Pt follows a normal random walk, i.e., Pt =
Po+r₁ + ... + rt with r₁, r2,... being IID N(μ, o²).
Po+r1+.
⚫ Suppose the VaR of rt is VaRq(rt) at level q, find the VaR of the price
in T days, i.e., VaRq(Pt – Pt–T).
-
• If ESq(rt) = A, find ES₁(Pt – Pt–T).
2 (Normal Distribution)
Let rt be a log return. Suppose that r₁, 2, ... are IID N(0.06, 0.47).
What is the distribution of rt (4) = rt + rt-1 + rt-2 + rt-3?
What is P(rt (4) < 2)?
What is the covariance between r2(2) = 1 + 12 and 13(2) = r² + 13?
• What is the conditional distribution of r₁(3) = rt + rt-1 + rt-2 given
rt-2 = 0.6?
3 (Sharpe-ratio) Suppose that X1, X2,..., is a lognormal geometric random
walk with parameters (μ, o²). Specifically, suppose that X = Xo exp(rı +
...Tk), where Xo is a fixed constant and r1, T2, ... are IID N(μ, o²). Find
the Sharpe-ratios of rk and log(Xk) — log(Xo) respectively, assuming the
risk free return is 0.
Chapter 1 Solutions
Finite Mathematics For The Managerial, Life, And Social Sciences
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.