Financial Management
Topic 1
Roadmap of the course
Portfolio theory & CAPM
Expected return =
Variance =
Investors problem within a portfolio: How to allocate my wealth? = optimization problem.
Computing portfolio expected returns: - - >
Correlation coefficient (p) = cov/(vol1*vol2)
A portfolio variance is more difficult.
The last part is the correlation-coëfficient.
Tangency portfolio!
Tangency portfolio -> Where the sharp (reward-to-volatility ratio is maximized
Sharp ratio = (E(rm) – rf) / Rm
Much assets -> difficulties with calculating. This is solved by using matrices in the calculation.
Vector of portfolio weights: W
Variance-covariance matrix: Ω
Portfolio variance: w’ Ωw
Investing in multiple asset could cause diversification benefits.
Diversification means that you diversify the idiosyncratic / firm-specific risk which leads to only
remaining the systematic risk.
Quiz final
Market risk premium: 8% -> find covariance and variance.
1
,Market Risk
Also called non-diversifiable risk, systematic risk
Attributable to market wide risk sources
Example: macroeconomic factors
Firm specific risk
Also called as diversifiable risk, unique risk, non-systematic ris
Risk is firm specific and the sources of risk are independent.
Example: success in R&D projects.
Potential diversification benefits arise when the assets are not perfectly correlated.
The portfolio risk does fall with diversification, but the power of diversification is limited by common
sources of risk. (in extreme cases: when the correlation is -1, we can construct a zero variance
portfolio -> Perfect Hedge!)
Minimum variance portfolio: the minimum variance portfolio is the portfolio composed of the risky
assets that has the smallest standard deviation, the portfolio with least risk.
(formula is derivec after applying the first order condition)
Separation theorem (portfolio theory) states that, under certain conditions, any investor's optimal
portfolio can be constructed by holding each of certain mutual funds in appropriate ratios, where the
number of mutual funds is smaller than the number of individual assets in the portfolio.
- All investors identify M because they want to be on the Capital Market line
- You choose to invest into the tangency portfolio.
Capital Asset Pricing Model (CAPM): a prediction about the relationship
between risk and expected return of an asset. The two functions:
A benchmark for rate of return
A guess of an expected return of an asset (in particular non-traded
assets).
What does CAPM say?
All investors will choose a market portfolio (M) with some
proportion (combining with some risk free asset
Capital Market line -> Investors’ optimal asset allocation line
Risk premium of the market portfolio M is proportional to its risk
and average risk aversion level of the investors
The risk premium on individual assets is proportional to risk
premium on market portfolio
2
,How do we measure β :
Is it possible to have a negative β?
Wiki: Negative betas are possible for investments that tend to go
down when the market goes up, and vice versa. There are few
fundamental investments with consistent and significant negative betas, but some derivatives like put
options can have large negative betas.
Example: gold market
A negative beta simply means that the stock is inversely correlated with the market.
A negative beta might occur even when both the benchmark index and the stock
under consideration have positive returns. It is possible that lower positive returns of
the index coincide with higher positive returns of the stock, or vice versa. The slope of
the regression line in such a case will be negative.
Roll’s critique: market portfolio is unobservable -> use a proxy like a stock index, but this
doesn’t include all assets.
Critics of CAPM
Is CAPM testable?
How to be sure about true expectations (e.g. E(r))
Roll’s critique -> market portfolio is unobservable
Why does CAPM fail from empirical tests?
Failure of data
Validity of the market proxy
Statistical methodology
CAPM is accepted as “the best available model”
Logic of decomposition of systematic and firm specific risk
The efficiency of market portfolio is not far from being valid.
3
, Topic 2: Valuing real assets
Chapter 9: Discounting and Valuation
The key idea in this chapter: Time has value!
Time value of money: how do we compare $$ today to $$ tomorrow!
Calculate
- Return: (P1-P0)/P0
- P1 = P0(1+r1)
- P0 = Pt / (1+r)^t
Compute the per period yield of a zero-coupon bond with a face
value of €100 at date 20 and a current price of €45.
- Nominal and real rates
- Inflation adjusted cash flows
You have to discount consistently -> Discounting nominal cash flows at nominal discount rates or
inflation-adjusted cash flows at the appropriately computed real interest rates generates the same
present value.
Perpetuity: PV = C/r
Growing perpetuity: PV = C / (r-g)
Annuity:
Growing annuities:
4
Topic 1
Roadmap of the course
Portfolio theory & CAPM
Expected return =
Variance =
Investors problem within a portfolio: How to allocate my wealth? = optimization problem.
Computing portfolio expected returns: - - >
Correlation coefficient (p) = cov/(vol1*vol2)
A portfolio variance is more difficult.
The last part is the correlation-coëfficient.
Tangency portfolio!
Tangency portfolio -> Where the sharp (reward-to-volatility ratio is maximized
Sharp ratio = (E(rm) – rf) / Rm
Much assets -> difficulties with calculating. This is solved by using matrices in the calculation.
Vector of portfolio weights: W
Variance-covariance matrix: Ω
Portfolio variance: w’ Ωw
Investing in multiple asset could cause diversification benefits.
Diversification means that you diversify the idiosyncratic / firm-specific risk which leads to only
remaining the systematic risk.
Quiz final
Market risk premium: 8% -> find covariance and variance.
1
,Market Risk
Also called non-diversifiable risk, systematic risk
Attributable to market wide risk sources
Example: macroeconomic factors
Firm specific risk
Also called as diversifiable risk, unique risk, non-systematic ris
Risk is firm specific and the sources of risk are independent.
Example: success in R&D projects.
Potential diversification benefits arise when the assets are not perfectly correlated.
The portfolio risk does fall with diversification, but the power of diversification is limited by common
sources of risk. (in extreme cases: when the correlation is -1, we can construct a zero variance
portfolio -> Perfect Hedge!)
Minimum variance portfolio: the minimum variance portfolio is the portfolio composed of the risky
assets that has the smallest standard deviation, the portfolio with least risk.
(formula is derivec after applying the first order condition)
Separation theorem (portfolio theory) states that, under certain conditions, any investor's optimal
portfolio can be constructed by holding each of certain mutual funds in appropriate ratios, where the
number of mutual funds is smaller than the number of individual assets in the portfolio.
- All investors identify M because they want to be on the Capital Market line
- You choose to invest into the tangency portfolio.
Capital Asset Pricing Model (CAPM): a prediction about the relationship
between risk and expected return of an asset. The two functions:
A benchmark for rate of return
A guess of an expected return of an asset (in particular non-traded
assets).
What does CAPM say?
All investors will choose a market portfolio (M) with some
proportion (combining with some risk free asset
Capital Market line -> Investors’ optimal asset allocation line
Risk premium of the market portfolio M is proportional to its risk
and average risk aversion level of the investors
The risk premium on individual assets is proportional to risk
premium on market portfolio
2
,How do we measure β :
Is it possible to have a negative β?
Wiki: Negative betas are possible for investments that tend to go
down when the market goes up, and vice versa. There are few
fundamental investments with consistent and significant negative betas, but some derivatives like put
options can have large negative betas.
Example: gold market
A negative beta simply means that the stock is inversely correlated with the market.
A negative beta might occur even when both the benchmark index and the stock
under consideration have positive returns. It is possible that lower positive returns of
the index coincide with higher positive returns of the stock, or vice versa. The slope of
the regression line in such a case will be negative.
Roll’s critique: market portfolio is unobservable -> use a proxy like a stock index, but this
doesn’t include all assets.
Critics of CAPM
Is CAPM testable?
How to be sure about true expectations (e.g. E(r))
Roll’s critique -> market portfolio is unobservable
Why does CAPM fail from empirical tests?
Failure of data
Validity of the market proxy
Statistical methodology
CAPM is accepted as “the best available model”
Logic of decomposition of systematic and firm specific risk
The efficiency of market portfolio is not far from being valid.
3
, Topic 2: Valuing real assets
Chapter 9: Discounting and Valuation
The key idea in this chapter: Time has value!
Time value of money: how do we compare $$ today to $$ tomorrow!
Calculate
- Return: (P1-P0)/P0
- P1 = P0(1+r1)
- P0 = Pt / (1+r)^t
Compute the per period yield of a zero-coupon bond with a face
value of €100 at date 20 and a current price of €45.
- Nominal and real rates
- Inflation adjusted cash flows
You have to discount consistently -> Discounting nominal cash flows at nominal discount rates or
inflation-adjusted cash flows at the appropriately computed real interest rates generates the same
present value.
Perpetuity: PV = C/r
Growing perpetuity: PV = C / (r-g)
Annuity:
Growing annuities:
4
