Test 1 Cheat Sheet
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Subject
Finance
Date
Feb 20, 2024
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docx
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Risk Premium:
Excess return required over a RF asset. = R-RF
Ex Post Returns:
R
E
=D1+P
END
-P
BEG
/ P
BEG *If you’re asked to find monthly returns you can’t find 1
st
month b/c you need previous month
AM= ΣX
i
/ t // GM= [(1+r
1
)(1+r
2
)(1+r
3
)..(1+r
t
)]
1/t
-1n
t= # of observations. GM takes into account compounding
RISK
Greater range= More risk. For risk we use STD as the measure. VAR= [(r
1
-R
AVE
)
2
+ (r
2
-R
AVE
)
2
+ (r
3
-R
AVE
)
2
] / T-1
// STD=√VAR. 68%=+/-1STD, 95%=+/-2STD, 99%=+/-3STD
Ex Ante:
ER= ΣR
j
x P
J (Expected return in scenario J x probability of state J)
VAR= ΣP
j
(R
J
-ER)
2
Portfolios
:
ER
P
= Σ (W
J
x ER
J
)
We can diversify portfolio w assets that aren’t positively correlated. Diversify by; geography, asset class, and sector
Portfolio Variance: VARP= W
A
2
STD
A
2 + W
B
2
STD
B
2 + 2W
A
W
B
COV
AB
// STD
P
= √VARP //
COV
AB
= ΣP
j
(R
AJ
-ER
A
)(R
BJ
-ER
B
) //
COV
AB
= CORR
AB
x STD
A
x STD
B
CORR
AB
= COV
AB
/ STD
A
STD
B
Risk & Return:
Risk= ER + U (Risk is made of expected risk, forecasted based on available info, and unexpected risk) Unexpected Risk can be 2 types: 1.
Systematic Risk: Non-diversifiable. Things going on in the economy we can’t help. Like inflation. Effects lots of stocks
2.
Unsystematic: Diversifiable. We can diversify away. Effects limited # of stocks. Can be eliminated by diverse portfolios
Measuring Systematic Risk: The Beta Coefficient. The beta of a security compares the volatility of its return compared to the market. B=1, asset has same systematic risk is same as market. B<1, asset has less systematic risk. B>1, asset has more systematic risk. (The beta of the market is always 1, beta of RF is 0) Total VS Systematic Risk:
Security
STD
Beta
Which has more total risk:
K
More systematic risk:
C
Which should have higher ER:
C
bc market doesn’t reward unnecessary (unsystematic) risk
C
20%
1.25
K
30%
0.95
B
i
= COV
im
/ STD
2
M =
(CORR
im
x STD
i
x STD
m
) / STD
2
M = (CORR
im
x STD
i
)/ STD
M
M= market, i= thing you’re comparing
Steps in Calculating Beta: 1.
Calculate ER for security & market
2.
Find COV
im
. COV
AM
= ΣP
j
(R
AJ
-ER
A
)(R
MJ
-ER
M
)
3.
Find variance of the market. VAR/STD
2
= ΣP
j
(R
J
-ER)
2
4.
Calculate beta
Portfolio Beta: It’s just the weighted average of all the betas in the portfolio. Beta and the Risk Premium:
The higher the beta, the higher the risk premium. Reward to Risk Ratio; Units of reward per unit of risk. =ER
A
-RF/ B
A
CAPM
: ER= RF + B(ER
M
-RF)
In an efficient market, RR=ER
ER>RR -> Undervalued, BUY
ER<RF -> Overvalued, SELL
EX: Suppose you consider buying a share of stock at $20. The stock is expected to pay a dividend of $2 next year and to sell for $22. The stock’s beta is 1.5. Government of Canada T-bills are yielding 3% and the market is expected to provide a risk premium of 8%. Is the stock overpriced, underpriced or correctly priced?
-
ER= 2 + 22 – 20/ 20 = 20%
(Expected Return)
-
RR= RF + B(ERM-RF)= 3% + 1.5(8%)= 15%
(Required Return)
EX: Beta= 0.8571. determine if the stock is over, under or correctly valued if it is trading at $35. Dividend of $1.50 to be paid in one year and expected to grow at 2% forever. The yield on T-bills is 3%. The market is expected to return 5.5% more than T-bills P=D1/ r-g
(We don’t have R, so we can solve for RR using CAPM)
RR= 3% + 0.8571(5.5%)= 7.714%
P= 1.50/( 0.07714-0.02)= $26.25
ER> RR, undervalued so we buy
$26.25 is the most you should pay to earn correct return for amount of risk. $35 would be overvalued.
EX: A company recently paid a dividend of $1.20. You expect dividends to grow at a rate of 5% per year forever. The company’s shares have a correlation with the market of 0.6. The standard deviation of the market is 2.4% and the standard deviation of the stock is 3.5%. The return on Tbills is 5% and the market risk premium is 4%. What would you be willing to pay for this stock?
P= D1/ r-g Again, we don’t have R so we can find RR with CAPM. RR= RF+ B(ERM-RF)
But we don’t have Beta, so we need to find Beta
B= CORR
SM
x STD
M
x STD
S
/ STD
2
M
= CORR
SM
x STD
S
/ STD
M
= 0.6 x 3.5%/ 2.4% =
0.875
We have beta so now we can find RR
RR= 5% +0.875(4%)= 8.5%
P=1.20(1.05)/ (0.085-0.05)= $36
EX A stock has a beta of 1.35 and an expected return of 16%. A risk-free asset currently earns 4.8%.
a)
What is the expected return on a portfolio that is equally invested in the two assets?
The expected return of the portfolio is:
E(Rp ) = .50(16) + .50(4.8) = 10.40%
b)
If the portfolio of the two assets has a beta of 0.95, what are the portfolio weights? We need to find the portfolio weights that result in a portfolio with a b of 0.95. We know the b of the risk-free asset is zero. We also know the weight of the risk-free asset is one minus the weight of the stock since the portfolio weights must sum to one, or 100 percent. So:
Bs = 1.35
ERS = 16%
BRF = 0
ERRF = 4.8%
We know:
Ws + WB = 1 or 100%
W
S
1.35 + W
RF
0= 0.95
So, 1.35Ws = .95
Ws = .7037 = 70.37%
and WRF = 1-.7037 = .2963 = 29.63%
c)
If a portfolio of the two assets has an expected return of 8%, what is the beta of the portfolio?
First, Find weights: ER
P
= W
S
16 +W
RF
4.8, 8= W
S
16 +W
RF
4.8
16W
S
+4.8(1-W
S
)= 8, 16W
S
+4.8 – 4.8W
S
= 8.
11.2W
S
=3.2. W
S
=28.57% W
RF
= 71.43%. Then just find weighted average of the portfolio Beta
B
P
= 0.2857(1.35) + 0.7143(0)= 0.386
EX:
Today, you sold 500 shares of Fundy Inc stock. Your total return on these shares is 25.72%. You purchased the 500 shares one year ago at a price of $43.00 per share. You received a total of $1,075 in dividends over the course of the year.
a) What is your dividend yield on this investment? b) What is your capital gains yield on this investment? c) What is the total market value of your 500 shares today? EX:
If you have $22,000 in total to invest and how much would you have to invest in each stock if you would like to have a portfolio return = 9.5%? 9.5% =WGME (8.5%) + WWMT (10.40%)
9.5% =WGME (8.5%) + (1- WGME )(10.40%)
9.5% = WGME (8.5%) + 10.40% - WGME (10.40%)
WGME (1.9%) = 0.90
WGME = 0.47368
WWMT = 1-0.47368 = 0.52632
EX
: You have $30,000 invested in stock SS and $20,000 invested in stock PP. Compute the expected return and total risk of this portfolio.
The standard deviation of Stock SS = 9.1864% and the standard deviation of Stock PP = 23.0366%.
Stock SS: = (0.2 × 24%) + (0.35 × 9%) + (0.30 × 3%) + (0.15 × -5%) = 8.10% Stock PP: = (0.2 × 45%) + (0.35 × 10%) + (0.30 × -10%) + (0.15 × -25%) = 5.75% And the expected return of the portfolio is:= $30,000/$50,000 (8.1%) + $20,000/$50,000 (5.75%), = .60(8.1%) + .40 (5.75%) = 7.16%.
Risk of the portfolio:
Covariance of returns:
.20 X (24%-8.1%) X (45% - 5.75%)+ .35 X (9%-8.1%) X (10% - 5.75%)+ .30 X (3%-8.1%) X (-10% - 5.75%)+ .15 X (-5%-8.1%) X (-25% - 5.75%)
Standard deviation = variance = √216.414 = 14.711%. EX:
Assuming Sirius stock is correctly pri4ced, according to CAPM; determine the beta for Sirius based on the following information:
• The expected market risk premium is 8%; standard deviation of the market is 12%, The return on Government of Canada T-Bills is 4%, Sirius recently paid a dividend of $4.50, Expected dividend growth rate is 3.6%, Current stock price is $36
Expected return:
E(R) = $4.50(1.036)/$36 + .036 = 16.55% (3 marks)
Required return:
16.55% = 4% + β[8%]
12.55% = β[8%]
β = 12.55%/8% = 1.56875 a) Dividend per share = $1,075 / 500 shares = $2.15 per share (1.5 marks)
Dividend yield = 2.15 / 43.00 = 5% (1.5 marks)
b) Capital Gain yield = 25.72% - 5% = 20.72% (2 marks)
c) New share price = $43 x (1+.2072) = $51.91 (1.5 marks)
Total market value = $51.91 x 500 shares = $25,955 (1.5 marks)
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