HW 1 Foundations of Finance NYU Stern Simone L. PDF

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This is homework number 1 on Statistics for the Foundations of Finance course at NYU Stern school of business with Professor Simone Lenzu...

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Ryan Messinger Professor Lenzu Foundations of Finance NYU Stern September 17th 2021 1. The Binomial Distribution a. The expected value of a fair coin is $ 0.50 if the value of heads is $ 2 and the value of tails is $ -1. b. The expected value of an unfair coin is $ -0.40 with these guidelines: 0.1*14 = 1.4, 0.9*2 = 1.8

2. Historical Stock Returns: UPLOADED ON EXCEL 3. Firms and economic uncertainty 1

a. x

p(x) 0 4 16 23

x*p(x)

0.31 0.25 0.38 0.06 Mean=

(x-mean)^2*p(x) 0 22.24731445 1 4.922851563 6 21.44677734 1.4375 13.25415039 8.44 Variance= 61.87109375 SD=

SQRT Variance 4.71670589 2.21875 4.631066545 3.640625

15.20714743

4. Firms and economic uncertainty 2 a. Expected return of IBM: (0*.1) + (.1*.5) + (.2*.4) = 0.13 ; Expected return of Dell: (-.1*.1) + (.1*.5) + (.3*.4) = 0.16 b.

IBM Variance Dell Variance IBM SD Dell SD

0.001633333 0.004233333 0.040414519 0.065064071

c. IBM Dell

IBM 0.001088889 0.001722222

Dell 0.002822222

d. IBM IBM Dell

Dell

1 0.982430421

1

5. Firms and economic uncertainty 3

a. Small Firm

Large Firm 0 1 2 3 4

Large - supply small - supply no shock small + supply large + supply

EV -4 -2 4 7 8

0 -2 8 21 32 EV = 59

b. Correlation: Small Firm Small Firm Large Firm

Covariance:

1 0.972271824

Large firm 1

Variance = 209.2

Large firm

Small Firm Small Firm Large Firm

2 6.6

23.04

4 7 8

8 21 32

c. 2 3 4

EV = 61

Variance = 144.3333333

d. Correlation Small Firm Small Firm Large Firm

Large firm

1 0.960768923

1

Covariance Small Firm Large Firm

Small Firm 0.666666667 1.333333333

Large firm

Small Firm

Large firm

2.888888889

e. Correlation Small Firm Large Firm Z

1 0.960768923 #DIV/0!

Z 1

#DIV/0!

1

Covariance Small Firm Large Firm Z

Small Firm 0.666666667 1.333333333 0

Large firm 2.888888889 0

Z

0...