Study Guides (390,000)

CA (150,000)

UTSG (10,000)

Rotman Commerce (300)

RSM332H1 (10)

Kevin Wang (5)

Final

# RSM332H1 Study Guide - Final Guide: Implied Volatility, Call Option, Capital Asset Pricing Model

by OC1798858

Department

Rotman CommerceCourse Code

RSM332H1Professor

Kevin WangStudy Guide

FinalThis

**preview**shows half of the first page. to view the full**1 pages of the document.**Portfolio Theory

! "#$ %

&! "&' %

(!)"(*+

,-

.$ /&

.,&

.0 /(

.,(1

.0 2/3/4,34 $ /5

.,5

. variance

,#

.$ /&

.,&

.0 /(

.,(

.0 2/&/(,&,(6&(

- Risk of the portfolios we obtain this way will

critically depend on the correlation 6&( .

CML: the tangent line from Rf to this M is known as

the capital market line, and is described by

!"#$ "7089:;9<

=:

,# [Sharpe ratio]

!"#$ "70 >! "5' "7+/5 and ,#$ /5,5

/&

?@- $AB

C;ADB

AD

CEAB

C;.ADB

MVP is the portfolios with the lowest possible risk and

therefore defines the lowest expected return we should be

willing to accept. We would invest in the efficient

portfolios as they offer the highest achievable expected

return for a given level of risk.

Utility Maximization

!"#$ /5! "50 F ' /5"7

/5$GHI;HJ

KAIC$LHM

K=:

[N O, less risk averse, take

more risk higher portfolio volatility and expected

return]

P ! "Q$ "70NRST "QU "5

V N&$GHW;HJ

XYZ>HWUHI+ [reward-risk ratio]

V N53[\]^ $GH_;HJ

XYZ H_UHI

$GH`;HJ

XYZ H`UHI

$GHI;HJ

AI

C

aST "3U "?$aST "3U /3"30 /4"4$ /3,3

.0 /4,34 $

11111111111111111111111111111163U5 ,3,5

!"5$ %

&! "&' %

(!)"(*

/&$GHB

bADB;G HD

bAB

C

GHD

bADB;AB

C;G HB

bAD

C;ADB

!"&

]$ ! "&' "7U 11,34 $ 6&(,&,(

! "5$ "70 N53[\]^,5

. à N53[\]^ $GHI;HJ

AI

C

/5$GHI;HJ

KAIC$KIWcdbe

K

If N f N53[\]^ (You are less risk averse than average

investors), /5g F, ,#g ,5,1! "#g ! "5

If N g N53[\]^, /5f F, ,#f ,5, !"#f ! "5

Why obtain the result (three Sharpe ratio)?

- among all portfolios on the Efficient Frontier, the

market portfolio is the one which has the highest

Sharpe ratio. The Sharpe ratio of the market portfolio

is the higher than that of any other portfolio or any

other individual risky assets.

Why aggregate risk aversion h all the same?

- if they are not equal, assets have the different

reward-risk ratio and there would be an arbitrage

trading which will lead them to be equal eventually.

Criticisms:

1. Returns do not follow the normal distribution. 2.

Parameters are not predictable in the long term (e.g., time-

varying correlations). 3. We don’t observe the market

portfolio. S&P500 is a proxy.

CAPM (measures performance of investment

strategies / the required return on a project)

SML:

- intuition: an asset commoves closely with the market is a risky

asset that should have a higher return. This is because investors

hold the market portfolio, following the Modern Portfolio Theory.

Because investors hold the market, they are concerned about an

asset that performs poorly when their portfolio (market portfolio)

performs poorly, Therefore, they care about the co-movement

between the return of an asset and the market returns. An asset

that doesn’t give you insurance and instead moves as the market

moves is a highly risky asset.

- the market equity premium is the slope of the SML, during

recessions, if the market equity premium becomes higher, given a

level of beta, an asset should have higher returns. This is because

overall market compensation increases for investors taking risk

even during recession times.

- !"QUX&-? $ "70 N53[\]^RST "QU "5

-"!"QUX&-? $ "7089:;9<

=:

iRST "QU "5"

$ "70 jk>! "5' "7+"

jk$lmn 9kU9:

=:

i$ 6QU5

A_

AI

- oQg F,"!"QUX&-? g 1! "5 aggresive

- oQf F, !"QUX&-? f 1! "5 defensive

- oQ$ F,"!"QUX&-? $ 1! "5"

oQ1determinants:

- nature of business [depends on economic condition]

- operating leverage [higher fixed cost, higher beta]

- financial leverage [volatilityp, riskp, higher beta]

- o-$ /o&0 >F ' /+o(

- !"#$ "70 o->! "5' "7+

qQ$ ! "Q' ! "QUX&-? ""

- gives abnormal returns that its riskiness(CAPM)

cannot explain [stock underpriced

rs$G-tEG>ut+

vEG>H_+

r

v$F 0 ! "Qw rs' ! xv

111111$ >F 0 "70 oQ! "5' "7w rs' !>xv+

Variance Composition:

Systematic risk = o&

.,?

. total risk = ,&

.

yz{az|}~•z $€D

CAM

C

AD

C

R-Square is 6Q U5 i$ oQ

.,5

.•,Q

.

Criticisms: technically, we

cannot test the CAPM

because we don’t observe the

market portfolio.

Option Pricing:

- getting a right/ having a legal obligation to buy/sell

the underlying asset at a pre-specified price and time.

- 买put: right to sell at strike price. 跌就挣。

- R‚$ƒ„…1)†U ‡‚' ˆ* 'R‚$ 'ƒ„…1)†U ‡‚' ˆ*

- r‚$ƒ„…1)†U ˆ ' ‡‚* 'r‚$ 'ƒ„…1)†U ˆ ' ‡‚*

- riskiness of option

Options in isolation are much riskier

than stocks. That is, with the same

amount of money invested in a

portfolio of options instead of a stock,

one can achieve a much higher risk exposure. Higher

riskiness is achieved via leverage

- Butterfly spreads:

ü buy call option with X1+sell 2 call options with

X2+buy call option with X3

ü I believe stock price will be stable (not volatile),

also I want to protect my downside.

- long straddle:

ü Buy call option with X2+ buy put option X1

ü I believe stock price is extremely volatile

- short straddle:

ü Sell call option with X2+sell put option X1

ü I believe stock price will be extremely stable.

Because it will be stable, I don’t care about my

downside, which can be negative infinite

- bull spread:

ü Buy$call$with$x1+$sell$call$with$x2$

ü Believe$price$will$be$X2.$Then$it$is$a$better$deal$

than$buying$call$option$with$x1$only$

Bull: Buy a call and sell a call with a higher strike price.

Bear: Buy a put and sell a put with a lower strike price.

- ‰ $ Š 0 ‹ ' Œ

>vE[+•

- call: strike price 20, 30: 20 will be more likely that

this option will pay off. Therefore, there is a higher

intrinsic value and option price should be higher than

the one with the

strike price of

$30.

If someone believes

that stock will be

around $15, the person would create this security. To

illustrate this point, suppose you buy only put option with the

strike price of $30, and the stock price turns out to be $15.

Your net payoff is $30−$15−$19.7 =−$4.7. Your net payoff

is negative even though the stock price goes down below the

strike price. However, if you construct the above security

(Bear spread), then your net payoff is$30−$15−$14.69 =

$0.31.

- Black-Scholes-Merton Model

Assume: 1. stocks are uncorrelated over timeàEMH

2. stock moves for infinitesimal small time (z;[^+

3. stock returns follow normal distribution

4. constant interest rate and volatility 5. No friction

‰ $ ‡sŽ•F ' ˆz;[‚Ž •2

•F $

•‘ ’“

”E [E•C

C‚

A‚ and •2 $ •F ' , –

a) Implied volatility:

1) Volatility for the BSM that makes the BSM price equal

the market call option price. It reflects investors expected

future volatility, whereas historical volatility captures past

volatility.

2) Smile and Smirk: Patterns that arise from the gap

between the normal distribution which the BSM is based on

and the investors’ expected distribution which is reflected in

the market option prices.

3) VIX: Implied volatility for S&P500 which aggregates all

option implied volatilities.

- —˜™š›œ $ •

sŽ•F ' ˆz;[‚ Ž>•2+

where •F $

•‘ ž“

”E [E•C

C‚

A ‚ and •2 $ •F ' , –

- Debt value: •

s'—˜™š›œ.

- Debt yield: Ÿ ¡ $ 1 v

‚¢£>¤3¥]1Z3¦§]

u]4^1Z3¦§]+

- Credit spread: Ÿ ¡ ' ¨

- Probability of default: F ' Ž>•2+

- the higher asset volatility, the higher equity value, the lower

debt value and the higher credit risk [call option prices

increase with the volatility and sell put option (part of debt

payoff) decrease with the volatility]/ the higher face value,

higher credit risk.

-higher volatility increases the expected equity payoff and

decreases the expected debt payoff. Since it leads to a higher

possibility that the equity holders make a lot of money while

their downside is limited. For debt holders, a higher

volatility translates in to a higher chance of not getting

money back. Therefore, they have to use a high discount

rate, resulting in a lower debt value

-The Firm A has a higher credit risk represented by the

higher probability of default, higher credit spread. The reason

for this is firm A total asset is more volatile than firm B,

therefore, there is a higher chance of not generating enough

cash flow to repay the debt.

Reason for market value < debt value?

You can think of this case as an out-of-the money call which

doesn’t have an intrinsic value. The reason for a positive equity

value is time value together with volatility. Even though the asset

value is lower than the debt claim, after two years, it is possible

that this firm will generate enough cash flow to cover the debt.

CAPM:

Beta different reason: We can think about the cyclicality of

these companies. We can imagine Starbucks profit is more

cyclical than McDonald as Starbucks have a premium price

policy.

Alpha different reason: This is because while their simple

average returns are similar, Starbucks have a higher beta. After

we consider the riskiness of Starbucks, Starbucks' stock didn't

perform well compared to McDonald. That is why alpha for

Starbucks is not statistically significant. This result implies that

Starbucks returns can be explained by its exposure to the market

risk and there is no additional compensation beyond the required

rate of returns implied by the CAPM.

Alpha CAPM: The sign is positive, which is consistent with the

CAPM because the slope of security market line is the market

equity premium which is positive.

How to use CAPM to measure mutual fund performance?

- By running a regression. Firstly, we compute the excess returns

of a mutual fund and the excess returns of the market for a certain

time period. Secondly, we run a regression of the excess returns

of a mutual fund on the excess returns of the market. Then the

intercept from the regression (alpha) captures the risk-adjusted

average returns in excess of the CAPM-implied expected returns.

Option Pricing:

Implied volatility and strike price: The pattern shows the

volatility smirk. That is, for options with low strike prices (in-the-

money call), the implied volatilities are high. For options with

high strike prices (out-the-money call), the implied volatilities are

higher than at-the-money call, but lower than in-the-money call

implied volatilities.

Reason: You can see this pattern because stock returns

distribution that investors expect is negatively skewed while the

BSM model assumes the normal distribution of stock returns.

When investors believe that an extreme negative event can

happen, they want to buy an option which can pay o during

extreme negative times. When investors buy those options, the

option prices increase. In order to match the observed high call

option price, the implied volatility must be high, which will drive

up the BSM model option price.

VIX related to the S&P500 returns: When overall stock prices

go down, firms have a higher debt-to-equity or debt-to-asset ratio.

When a debt accounts for a greater portion of firm asset, a credit

risk increases, which is factored into the volatility (leverage

effect). Another reason is risk aversion and uncertainty. When

stock prices go down, investors become more risk averse. A less

risk-taking behavior can lead to a further drop in the stock prices

and therefore uncertainty of the market increases, which is

factored into the volatility.

###### You're Reading a Preview

Unlock to view full version