Midterm exam
Animal spirits
Lecture 15 — Midterm + behavioral finance
FNCE 4030, Fall 2015
Diego Garcı́a
Leeds School of Business
University of Colorado at Boulder
October 15th, 2015
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
Midterm exam
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Animal spirits
Outline
1
Midterm exam
Midterm exam
2
Animal spirits
Animal spirits
Handouts: class slides, midterm solutions.
Animal spirits case solutions, two cases for next week.
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
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Midterm exam
Animal spirits
Midterm exam
Mean of 49 (70%), SD of 14 (20%).
I thought the class did quite well.
If you are below 30, please come see me.
Perhaps another midterm before the final?
Hedging/diversifying: 3 exams versus 2 exams.
More practice.
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
Midterm exam
3 / 17
Animal spirits
Question 1
Bond A
Bond B
Bond C
Maturity
3
3
1
Annual coupon rate
2%
4%
8%
Price
847.81
901.78
1058.82
Questions:
Term structure.
Forward rates.
Duration.
Pricing and replication/arbitrage.
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
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Midterm exam
Animal spirits
Question 1 (a)-(b)
Term structure from PV formulae:
P1 =
P2 =
P3 =
20
20
1020
+
+
= 847.81
(1 + r1 ) (1 + r2 )2 (1 + r3 )3
40
1040
40
+
+
= 901.78
(1 + r1 ) (1 + r2 )2 (1 + r3 )3
1080
= 1058.82
(1 + r1 )
Spot rates are r1 = 2%, r2 = 4%, and r3 = 8%.
(1 + r2 )2 = (1 + r1 )(1 + f1,2 )
(1 + r3 )3 = (1 + r2 )2 (1 + f2,3 )
so that f1,2 = 6% and f2,3 = 16.5%.
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
Midterm exam
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Animal spirits
Question 1 (c)-(d)
Duration question: C lowest (highest coupon, lowest maturity),
then B (same maturity, higher coupon), so A is the most
sensitive.
Pricing bonds:
V=
50
50
1500
+
+
= 928.77
(1 + r1 ) (1 + r2 )2 (1 + r3 )3
Replication:
t=1
20x + 40y + 1080z = 50
t=2
20x + 40y = 50
t=3
1020x + 1040y = 1050
My calculations suggest x = −0.5, y = 1.5 and z = 0 do the job.
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
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Midterm exam
Animal spirits
Question 1 (e)
Arbitrage!
Buy bond
Buy 0.5 Bond A
Sell 1.5 Bond B
Net
t=0
−860
−423.90
1352.68
68.77
t=1
50.00
10
−60
0
t=2
50.00
10
−60
0
t=3
1050.00
510
−1560
0
Recipe: buy the cheap security (the 5% 3y bond), and sell the
expensive one (the replicating portfolio).
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
Midterm exam
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Animal spirits
Question 2
Red stocks
Green stocks
Mean
0.10
0.10
Stand. dev.
0.2
0.3
Corr.
0.9
0.5
Corr. between red/green is 0.4. Risk-free asset at 5%.
Questions:
Compute probabilities.
Measure risk of two stocks.
Find optimal mix of two stocks.
Find optimal mix of two “funds” (***).
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
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Midterm exam
Animal spirits
Question 2 (a)-(b)
P(Pt ≥ 7.5)
P(Pt ≥ 10)
RED001
26.9%
2.0%
GRE999
15.4%
2.4%
Why does the answer flip?
The variance of the portfolio of two red (green) stocks is
var(rRP ) = w2 0.22 + (1 − w)2 0.22 + 2w(1 − w)0.9(0.2)(0.2) = 0.038,
2
2
2
2
var(rG
P ) = w 0.3 +(1−w) 0.3 +2w(1−w)0.5(0.3)(0.3) = 0.0675,
so that SD(rRp ) = 19.49%, and SD(rG
p ) = 25.98%.
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
Midterm exam
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Animal spirits
Question 2 (c)
Now we mix two risky assets:
var(rp ) = w2 0.22 + (1 − w)2 0.32 + 2w(1 − w)0.4(0.2)(0.3);
Maximize the Sharpe ratio to find w = 0.804 in the red stock,
and 1 − w = 0.196 in the green stock. Why the tilt?
Maximize expected utility:
1
Ui = x0.10 + (1 − x)0.05 − Ai x2 0.1922
2
so that
x=
c Diego Garcı́a, FNCE 4030, Fall 2015
0.05
= 1.36,
0.1922
Lecture 15 — Midterm + behavioral finance
10 / 17
Midterm exam
Animal spirits
Question 2 (d)
“New” problem: now you can invest in a portfolio of N reds,
and a portfolio of N greens.
1
(N − 1)
0.32 +
0.5(0.32 ) ≈ 0.036
N
N
1
(N − 1)
var(rRp ) = 0.22 +
0.9(0.22 ) ≈ 0.045
N
N
Covariance is 0.4(0.3)(0.2).
var(rG
p) =
Maximize the Sharpe ratio to find w = 0.64 in the red fund, and
1 − w = 0.36 in the green fund. Why did the tilt change?
Maximizing expected utility x = 1.58: why more aggressive
now?
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
Midterm exam
11 / 17
Animal spirits
Going forward
Two themes:
Derivatives (8-10 lectures).
Empirical facts/portfolio evaluation (4-5 lectures).
Derivatives introduction:
Replication in a static framework.
Dynamic trading strategies and Black-Scholes.
Applications: risky bonds, real options.
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
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Midterm exam
Animal spirits
Animal spirits case
Data on weather (from NOAA).
Temperature (mean/max/min), wind speeds, visibility,
snow, rain, fog, . . . .
Data on DJIA.
Long time-series, NYSE open on Saturdays!?
Questions:
Document day-of-the-week effect.
Are weather and stock returns really related?
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
Midterm exam
13 / 17
Animal spirits
Data analysis approaches
This case can be done in Excel.
With the barebones version it would be tricky.
We should try.
Much easier to use a Statistical package.
Get as many tools as you can while at CU-Boulder!
Data analysts are in excess demand in today’s job market.
My solutions use R.
Open-source, most commonly used Statistics package.
Stata, SAS, etc are fine too.
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Lecture 15 — Midterm + behavioral finance
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Midterm exam
Animal spirits
Monday blues
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Means
−0.101%
0.035%
0.051%
0.023%
0.060%
0.080%
Reg. coef
−
0.142%
0.147%
0.124%
0.165%
0.181%
Returns on Mondays are significantly lower than any other day
of the week.
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
Midterm exam
15 / 17
Animal spirits
Weather and stock returns
Rt = α + β > Wt + t ;
Variable
temperature
dewpoint
visibility
maxwind
maxgust
maxtemp
mintemp
precipitation
snow
β
0.024
0.000
0.037
−0.010
−0.002
0.002
−0.014
0.004
0.034
t-stat
0.76
0.02
1.88
−0.36
−0.10
0.15
−0.83
0.34
1.91
Snow and visibility marginally significant.
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
16 / 17
Midterm exam
Animal spirits
Wrap-up
Today:
Midterm recap.
Weather/DoW and stock returns.
Coming up: derivatives!
Trading strategies using options.
Rinconete case.
Put-call parity.
Rocinante case.
Prep the cases.
Use book/internet for hints.
c Diego Garcı́a, FNCE 4030, Fall 2015
Lecture 15 — Midterm + behavioral finance
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