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Modern Finance > Week 2- Portfolio Theory > Flashcards

Week 2- Portfolio Theory Flashcards

1
Q

What are the two types of risk?

A

Systematic risk and unsystematic risk

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2
Q

What is the difference between speculation and gambling

A

Speculation occurs in spite of risk due to the perception of a favourable risk-return trade off, whereas in gambling risk is assumed for the enjoyment of risk itself. Effectively the central difference is the lack of β€œcommensurate gain”

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3
Q

What is the utility function we assume that investors assign to their competing portfolios?

A

π‘ˆ = 𝐸(π‘Ÿ) βˆ’ 1/2𝐴𝜎^2

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4
Q

In the utility function: π‘ˆ = 𝐸(π‘Ÿ) βˆ’ 1/2𝐴𝜎^2, what does everything stand for?

A
  • π‘ˆ = Utility value
  • 𝐸(π‘Ÿ) = Expected return
  • 𝐴 = Index of the investor’s risk aversion
  • 𝜎2 = Variance of returns
  • Β½ = Scaling factor
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5
Q

What are the 3 kinds of investors? How does their A index demonstrate this?

A
  • Risk Averse (A>0)
  • Risk Neutral (A=0)
  • Risk Loving (A<0)
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6
Q

How do risk averse individuals view risk?

A

Risk-averse investors consider risky portfolios only if they provide
compensation for risk via a risk premium.

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7
Q

How do risk neutral individuals view risk?

A

Risk-neutral investors find the level of risk irrelevant and consider
only the expected return of risk prospects.

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8
Q

How do risk loving individuals view risk?

A

Risk lovers are willing to accept lower expected returns on
prospects with higher amounts of risk.

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9
Q

How do we find the risk-free rate?

A

Risk-free Rate = Expected Return - Risk Premium

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10
Q

What is the portfolio return?

A

A simple weighted average of the proportion invested in each stock

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11
Q

What does the risk of a portfolio depend on?

A
  • The risk of the individual stocks in the portfolio; and
  • T he correlations between the stocks.
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12
Q

So how do we work out the return of a portfolio, say of in a portfolio with an 80:20 split between stocks A and B, stock A with 5.96% return and stock B with 9.10% return?

A

portfolioAB= (0.8 Γ— 5.96) + (0.2 Γ— 9.1) = 6.59%

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13
Q

For a portfolio with 2 Stocks, A and B, what is the covariance of Stocks A and B? How about the covariance between Stocks B and A?

A

𝜎𝐴B = 𝜌𝐴B𝜎𝐴𝜎B

𝜎B𝐴 = 𝜌B𝐴𝜎B𝜎𝐴
Note that these are identical
Additionally, if there are multiple events with different probabilities, these all need adding up

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14
Q

What is the covariance a product of?

A

Covariance can be expressed as the product of the correlation coefficient 𝜌𝐴B and the two standard deviations 𝜎.

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15
Q

What is the purpose of diversification?

A

Diversification is the process of combining securities in a portfolio with the aim of reducing total risk, but without sacrificing the portfolio return.

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16
Q

What is key for why diversification works?

A

Diversification works because stock prices do not move in perfectly in phase with one another.

As some stock prices are moving upwardly others are moving in the
opposite direction.

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17
Q

What happens to unsystematic risk as the number of investments in a portfolio increases?

A

It decreases, this is called portfolio diversification of risk

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18
Q

What is the difference between systematic and unsystematic risk?

A

Unsystematic risk is a risk specific to a company or industry, while systematic risk is the risk tied to the broader market, such as changes in business cycles or govt policy.

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19
Q

What are other names for systematic and unsystematic risk?

A

Market and Unique risk

20
Q

What does total risk =?

A

Total Risk = Systematic (market) Risk + Unsystematic (unique) Risk

21
Q

What must the correlation coefficient 𝜌𝐴B stay between?

A

-1 < 𝜌𝐴B < 1

22
Q

Can unsystematic risk be diversified away if 𝜌𝐴B = +1?

A

No unsystematic risk can be diversified away in this situation (however this rarely happens)

23
Q

Can unsystematic risk be diversified away if 𝜌𝐴B = -1?

A

In this situation, all unsystematic risk will be diversified away

24
Q

Can unsystematic risk be diversified away if 𝜌𝐴B = 0?

A

In this situation there is no correlation between the returns of the 2 securities.

25
Q

How much risk roughly on a single share is based on systematic risk?

A

About 35%

26
Q

When creating a 2 stock portfolio, do we want 𝜌𝐴B to be +1 or -1? Why?

A

-1, so we can diversify all unsystematic risk as the stock’s performances alter perfectly with each other, ie as one goes up, the other falls by an equal amount.

27
Q

What do the size of diversification benefits depend on?

A

The correlation between the 2 stocks

28
Q

Why are downward-sloping portfolio possibility curves inefficient?

A

As they are obtaining a lower return for the same amount of risk than upward-sloping portfolio possibility curves.

29
Q

What does the Efficient Frontier consist of?

A

The Efficient Frontier consists of an envelope of all portfolios that lie between the minimum variance and maximum return portfolios.

30
Q

Name 3 features of Markowitz’s Portfolio Theory (1952):

A
  • Portfolio consisting of N stocks
  • Efficient set when there is a riskless asset
  • Market equilibrium
31
Q

In a portfolio with a risky and a risk-free asset, what is the expected return? What does the slope mean?

A

𝑅𝑝 = 𝑅𝑓 +((𝑅̄1 βˆ’ 𝑅𝑓)/𝜎1) * 𝜎p
- The slope (𝑅̄1 βˆ’ 𝑅𝑓)/𝜎1) os the extra unit per additional unit of risk (ie the Sharpe ratio)

32
Q

In a portfolio with a risky and a risk-free asset, what is the standard deviation?

A

πœŽπ‘ƒ = πœ™1𝜎1 where πœ™1 is the proportion of wealth held in the risky stock

33
Q

What does the Capital Market Line (CML) show?

A

That investors can both lend and borrow at a risk-free rate of return

34
Q

What is true about the market portfolio (m)?

A

There are no risk-free assets, only risky assets.

35
Q

Why would leverage be employed?

A

To enhance return

36
Q

What does the market portfolio maximise, and what is it on a diagram?

A

The market portfolio will maximise the Sharpe ratio and lies at the point of tangency
between the Capital Market Line and the Efficient Frontier.

37
Q

What about portfolios on the CML derived by?

A

/borrowing and lending at the riskless rate of interest in the capital market.

38
Q

What is the optimal portfolio?

A

This is specific for each investor, given their level of risk.

39
Q

What does the Separation Theorm (Tobin, 1958) state?

A

Whatever the risk preferences of individuals, in equilibrium, all investors hold portfolio m (the market portfolio) then either borrowing or lending at the riskless rate.

40
Q

What is the market portfolio?

A

The market portfolio is the portfolio of all stocks in the economy with weights equal to their relative market values.

41
Q

What are 2 criticisms of the Separation Theorem?

A
  • It’s unrealistic for an investor to hold every single stock
  • It is unrealistic for investors to be able to borrow or lend at the risk-free rate
42
Q

What is the market price of risk equal to? So what is the equation?

A
  • The market price of risk is equal to the slope of the CML.
  • 𝑅𝑝 = 𝑅𝑓 +((𝑅̄m βˆ’ 𝑅𝑓)/𝜎m) * 𝜎p
43
Q

How do we calculate the correlation between stocks A and B?

A

Work out the covariance between A and B and divide by the total of the standard deviations of A and B

44
Q

How do we work out portfolio variance?vGive the steps. What about for standard deviation?

A
  • (Decimal percentage invested in Stock A multiplied by deviation of A)^2
  • (Decimal percentage invested in Stock B multiplied by deviation of B)^2
  • 2 x decimal invested in A x decimal invested in B x covariance of AB
  • Add all these up
45
Q

If you have multiple portfolios, each with different risk premiums per unit of risk, which is most likely to be the market portfolio?

A

The portfolio with the highest risk-free premium per unit of risk is most likely to be the market portfolio.

46
Q

What is the Sharpe ratio?

A

Risk premium/Standard deviation

Modern Finance (9 decks)

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