Advanced Financial Economics Lectures
Sometimes: look at Topics in financial economics.
Book: Cuthbertson, K. and Nitzsche, D. (2004) ‘Quantitative Financial Economics’, second edition,
WILEY Publisher.
Content:
The course “Advanced Financial Economics” covers some essential and relatively advanced topics in
financial economics. These topics will include a number of classical issues in financial economics. This
course will try to balance theories and empirical works because this is necessary for a solid
understanding of financial economics.
After following this course, you should be able to:
1. understand valuation principles, equity premium puzzle, and excess volatility; perform empirical
tests of the above concepts.
2. derive, discuss, and test empirically Capital Asset Pricing Model (CAPM); address the limitation in
the application of CAPM in practice; have an understanding of alternative models of CAPM, such as
consumption-based CAPM.
3. understand and assess factor models; statistically analyse real data using factor models.
4. understand the source of inter-temporal discounting; assess different models of intertemporal
choices.
5. critically assess and discuss the most recent developments in financial economics, and
communicate those messages to others via a presentation.
Week 1) Basic and utility functions (Ch. 1)
a. Basic concepts in finance
b. Utility functions
29-1, L1: The basics (Asset Pricing and Portfolio Theory)
Contents:
- Prices, returns, HPR.
- Basic concepts : compounding, discounting, NPV, IRR.
- Key questions in finance.
- Investment appraisal.
- Valuating a firm.
Calculating rates of return (Ch. 2.2)
- Financial data is usually provided in forms of prices.
* e.g. bond price, share price, FX, stock price index, etc.
- Financial analysis is usually conducted on rate of return: transform prices into returns.
* prices are not stationary, the best predictor of tomorrow’s price is today’s price
* this gives statistical issues because you should work with stationary data
* also, returns are easier to compare (more transparent)
- Stationary: statistical properties (mean and variance) are the same throughout the series,
irrespective of time.
Intern gebruik
, How to transform Prices → Rate of Return
Arithmetic rate of return: Rt = (Pt - Pt-1)/Pt-1
But we should use continuous compounded rate of return:
→ Rt = ln(Pt/Pt-1) = ln(Pt)-ln(Pt-1) and Pt = Pt-1*e(1*Rt).
- Get similar results, especially for small price changes.
- However, geometric rate of return preferred: more economic meaningful (no negative
prices) and symmetric (important for FX)
→ An example: P0=1, P1=0.7, P2=1, R1=-0.30, R2=0.43
- Arithmetic average: (R1 + R2)/2= 0.065
- Does it mean an initial investment of 100 will be W=100*(1+0.065)2=113?
* this is not correct, thus arithmetic average is misleading!
- Geometric mean: sqrt[(1+ R1)(1+ R2)] = 1
[(1+ R1)(1+ R2) … (1+ Rn)]1/n – 1
SLIDE 6 & 7: why we use returns and not index price directly!!
- Prices are not stationary, they have an uprising trend. With this you cannot write
regressions.
- Returns are stationary, there’s no obvious trend.
* roughly a horizontal trend with the constant variance
Finance: What are the key questions?
‘Big Questions’: Valuation
How do we decide on whether …
- … to undertake a new (physical) investment project?
- ... to buy a potential ’takeover target’?
- … to buy stocks, bonds and other financial instruments (including foreign assets)?
→ To determine the above we need to calculate the ‘correct’ or ‘fair’ value V of the future
cash flows from these ‘assets’.
If V > P (price of stock) or V > capital cost of project then purchase ‘asset’.
‘Big Questions’: Risk
For the valuation we have to understand the risk: how do we take account of the ‘riskiness
of the future cash flows when determining the fair value of these assets (e.g. stocks,
investment project)?
→ Use Discounted Present Value Model (DPV) where the discount rate should reflect the
riskiness of the future cash flows from the asset: CAPM.
- More risk, higher discount rate.
* DF=1/(1+Ra)T = e(-T*Ra)
- But what rate of return to use to discount: CAPM.
* Ra - rf = betaa*(Rm-rf)
‘Big Questions’
1. Portfolio Theory: can we combine several assets in order to reduce risk while still
maintaining some ‘return’?
- Portfolio theory, international diversification.
Intern gebruik
, 2. Hedging: can we combine several assets in order to reduce risk to (near) zero?
- Hedging with derivatives (options, futures, swaps, etc.).
3. Speculation: can ‘stock pickers’ ‘beat the market’ return (i.e. index tracker on S&P500),
over a run of bets, after correcting for risk and transaction costs?
Compounding, Discounting, NPV, IRR
Compounding Frequencies
Interest payment on a £10,000 loan (r = 6% p.a.).
- Simple interest £ 10,000 (1 + 0.06) = £ 10,600
- Half yearly compounding £ 10,000 (1 + 0.06/2)2 = £ 10,609
- Quarterly compounding: £ 10,000 (1 + 0.06/4)4 = £ 10,614
- Monthly compounding £ 10,000 (1 + 0.06/12)12 = £ 10,617
- Daily compounding £ 10,000 (1 + 0.06/365)365 = £ 10,618.31
- Continuous compounding £ 10,000 e0.06 = £ 10,618.37
→ The more frequent you earn interest, the more you earn.
Discounted Present Value (DPV)
What is the value today of a stream of payments (assuming constant discount factor and
non-risky receipts)?
- Discount all future cash flows with a certain discount rate.
- Discounting converts all future cash flows on to a common basis (so they can then be
‘added up’ and compared).
DPV = V1/(1+r) + V2/(1+r)2 + …
= d1 V1 + d2 V2 + …
d = ‘discount factor’ < 1
Vn = certain payment in n years time
Investment Appraisal (NPV and DPV) OVERGESLAGEN
Consider the following investment:
- Capital Cost: Cost = $2,000 (at time t= 0)
- Cashflows:
* year 1: V1 = $1,100
* year 2: V2 = $1,210
- Net Present Value (NPV) is defined as the discounted present value less the capital costs.
* NPV = DPV – Cost
- Investment Rule: if NPV > 0 then invest in the project.
* to see whether an investment is worthwhile
→ Depends on the discount rate: comes from cost of capital or CAPM.
E.g. when r = 0.05:
- DPV = V1/(1+r) + V2/(1+r)2 = 1,100/1.05 + 1,210/1.052 = 2,145.12
- NPV = 2,145.12 – 2,000 > 0
Intern gebruik
, Internal Rate of Return (IRR)
- IRR is also called YTM, it’s an alternative way (to DPV) of evaluating investment projects.
- Compares expected cash flows (CF) and capital costs (KC)
→ Example:
- KC = - $ 2,000 (t = 0)
- CF1 = $ 1,100 (t = 1)
- CF2 = $ 1,210 (t = 2)
- Then: NPV (DPV - cost) = -$2,000 + ($ 1,100)/(1 + r)1 + ($ 1,210)/(1 + r)2
- IRR: $2,000 = ($ 1,100)/(1 + y)1 + ($ 1,210)/(1 + y)2
* what kind or IRR/YTM (y) will make the DPV equal to the KC
* thus, NPV = 0
* IRR tells you what the return is on average
Graphical Presentation : NPV and the Discount Rate
Thus, IRR makes the NPV equal to zero.
DPV = costs.
Investment Decision OVERGESLAGEN
- Thus, invest in the project if:
* DPV > KC or NPV > 0
* IRR > r
* if DPV = KC or if IRR is just equal the opportunity cost of the fund, then investment project
will just pay back the principal and interest on loan.
- If DPV = KC → IRR = r.
Summary of NPV and IRR OVERGESLAGEN
- NPV and IRR give similar results for independent projects with ‘normal cash flows’.
- For cash flows which change sign more than once, the IRR gives multiple solutions and
cannot be used → use NPV.
* NPV is more robust and flexible
- For mutually exclusive projects use the NPV criterion.
Stocks
For stocks, we often need to calculate the fundamental values.
- Vt=Et[Dt+1/R1+Dt+2/R2+…].
* value of a stock equals the discounted present value of future dividends
- When no systematic returns from tradings: Pt=Vt (with systematic returns?).
Gordon growth model: calculates a stock’s fundamental value by summing its discounted
dividends that grow at a constant rate.
- when dividends (D) grow in a certain rate (g), the value of a stock is equal to: V0 = P0 =
D0(1+g)/(R-g).
* R is the (known) required rate of return and g the expected growth of the dividends
- Shows that the price-dividend ratio: P/D = (1+g)/(R-g), is a constant that’s positively related
to growth of the company and negatively to the cost of capital.
* calculating the P/D of a firm, you can infer how much growth people are expecting from
Intern gebruik
, the firm
* when P/D is very high: can be only sustained when company grows very hard
* thus, when firm doesn’t grow as hard as expected, price drops
Systematic trading returns
Solve by backwards induction: all traders are smart and know the others are smart.
Works ONLY if you know that everyone knows that everyone is smart.
31-1, L2: Utility and Risk Aversion
Contents:
- Introduction to utility theory.
- Relative and absolute risk aversion.
- Different forms of utility functions.
- Empirical evidence.
- How useful are the general findings?
* equity premium puzzle
* risk free rate puzzle
Introduction
- Many different investment opportunities with different risk – return characteristics.
- Things will be much simpler if investors are risk neutral.
- General assumption in financial market: ‘people like returns, dislike risk’.
- Preferences of investors (like more to less).
Risk Premium and Risk Aversion
- Risk free rate of return: rate of return which can be earned with certainty (i.e σ = 0).
* e.g a 3 months T-bill
* asset with no risk still earns a return due to time preference
- Risk premium: expected return in excess of the risk free rate (i.e. ERp – rf).
* proportional to the risk people perceive
- Risk aversion: measures the reluctance by investors to accept (more) risk.
* ‘high number’: risk averse
* ‘low number’: less risk averse
→ Example:
- ERp - rf = 0.005 A σ2p
* expected return depends on risk attitude (A) times riskiness of
the portfolio (σ2p)
* thus, more risk averse, you require higher risk premium
- A = (ERp - rf) / (0.005 σ2p)
- SR = (ERp - rf) / σ2p
Indifference curve of this particular preference:
- When σ increases, you require higher return to be indifferent between the two assets.
* non-linear (σ2p): the larger it gets, the more additional higher return you want
Intern gebruik
Sometimes: look at Topics in financial economics.
Book: Cuthbertson, K. and Nitzsche, D. (2004) ‘Quantitative Financial Economics’, second edition,
WILEY Publisher.
Content:
The course “Advanced Financial Economics” covers some essential and relatively advanced topics in
financial economics. These topics will include a number of classical issues in financial economics. This
course will try to balance theories and empirical works because this is necessary for a solid
understanding of financial economics.
After following this course, you should be able to:
1. understand valuation principles, equity premium puzzle, and excess volatility; perform empirical
tests of the above concepts.
2. derive, discuss, and test empirically Capital Asset Pricing Model (CAPM); address the limitation in
the application of CAPM in practice; have an understanding of alternative models of CAPM, such as
consumption-based CAPM.
3. understand and assess factor models; statistically analyse real data using factor models.
4. understand the source of inter-temporal discounting; assess different models of intertemporal
choices.
5. critically assess and discuss the most recent developments in financial economics, and
communicate those messages to others via a presentation.
Week 1) Basic and utility functions (Ch. 1)
a. Basic concepts in finance
b. Utility functions
29-1, L1: The basics (Asset Pricing and Portfolio Theory)
Contents:
- Prices, returns, HPR.
- Basic concepts : compounding, discounting, NPV, IRR.
- Key questions in finance.
- Investment appraisal.
- Valuating a firm.
Calculating rates of return (Ch. 2.2)
- Financial data is usually provided in forms of prices.
* e.g. bond price, share price, FX, stock price index, etc.
- Financial analysis is usually conducted on rate of return: transform prices into returns.
* prices are not stationary, the best predictor of tomorrow’s price is today’s price
* this gives statistical issues because you should work with stationary data
* also, returns are easier to compare (more transparent)
- Stationary: statistical properties (mean and variance) are the same throughout the series,
irrespective of time.
Intern gebruik
, How to transform Prices → Rate of Return
Arithmetic rate of return: Rt = (Pt - Pt-1)/Pt-1
But we should use continuous compounded rate of return:
→ Rt = ln(Pt/Pt-1) = ln(Pt)-ln(Pt-1) and Pt = Pt-1*e(1*Rt).
- Get similar results, especially for small price changes.
- However, geometric rate of return preferred: more economic meaningful (no negative
prices) and symmetric (important for FX)
→ An example: P0=1, P1=0.7, P2=1, R1=-0.30, R2=0.43
- Arithmetic average: (R1 + R2)/2= 0.065
- Does it mean an initial investment of 100 will be W=100*(1+0.065)2=113?
* this is not correct, thus arithmetic average is misleading!
- Geometric mean: sqrt[(1+ R1)(1+ R2)] = 1
[(1+ R1)(1+ R2) … (1+ Rn)]1/n – 1
SLIDE 6 & 7: why we use returns and not index price directly!!
- Prices are not stationary, they have an uprising trend. With this you cannot write
regressions.
- Returns are stationary, there’s no obvious trend.
* roughly a horizontal trend with the constant variance
Finance: What are the key questions?
‘Big Questions’: Valuation
How do we decide on whether …
- … to undertake a new (physical) investment project?
- ... to buy a potential ’takeover target’?
- … to buy stocks, bonds and other financial instruments (including foreign assets)?
→ To determine the above we need to calculate the ‘correct’ or ‘fair’ value V of the future
cash flows from these ‘assets’.
If V > P (price of stock) or V > capital cost of project then purchase ‘asset’.
‘Big Questions’: Risk
For the valuation we have to understand the risk: how do we take account of the ‘riskiness
of the future cash flows when determining the fair value of these assets (e.g. stocks,
investment project)?
→ Use Discounted Present Value Model (DPV) where the discount rate should reflect the
riskiness of the future cash flows from the asset: CAPM.
- More risk, higher discount rate.
* DF=1/(1+Ra)T = e(-T*Ra)
- But what rate of return to use to discount: CAPM.
* Ra - rf = betaa*(Rm-rf)
‘Big Questions’
1. Portfolio Theory: can we combine several assets in order to reduce risk while still
maintaining some ‘return’?
- Portfolio theory, international diversification.
Intern gebruik
, 2. Hedging: can we combine several assets in order to reduce risk to (near) zero?
- Hedging with derivatives (options, futures, swaps, etc.).
3. Speculation: can ‘stock pickers’ ‘beat the market’ return (i.e. index tracker on S&P500),
over a run of bets, after correcting for risk and transaction costs?
Compounding, Discounting, NPV, IRR
Compounding Frequencies
Interest payment on a £10,000 loan (r = 6% p.a.).
- Simple interest £ 10,000 (1 + 0.06) = £ 10,600
- Half yearly compounding £ 10,000 (1 + 0.06/2)2 = £ 10,609
- Quarterly compounding: £ 10,000 (1 + 0.06/4)4 = £ 10,614
- Monthly compounding £ 10,000 (1 + 0.06/12)12 = £ 10,617
- Daily compounding £ 10,000 (1 + 0.06/365)365 = £ 10,618.31
- Continuous compounding £ 10,000 e0.06 = £ 10,618.37
→ The more frequent you earn interest, the more you earn.
Discounted Present Value (DPV)
What is the value today of a stream of payments (assuming constant discount factor and
non-risky receipts)?
- Discount all future cash flows with a certain discount rate.
- Discounting converts all future cash flows on to a common basis (so they can then be
‘added up’ and compared).
DPV = V1/(1+r) + V2/(1+r)2 + …
= d1 V1 + d2 V2 + …
d = ‘discount factor’ < 1
Vn = certain payment in n years time
Investment Appraisal (NPV and DPV) OVERGESLAGEN
Consider the following investment:
- Capital Cost: Cost = $2,000 (at time t= 0)
- Cashflows:
* year 1: V1 = $1,100
* year 2: V2 = $1,210
- Net Present Value (NPV) is defined as the discounted present value less the capital costs.
* NPV = DPV – Cost
- Investment Rule: if NPV > 0 then invest in the project.
* to see whether an investment is worthwhile
→ Depends on the discount rate: comes from cost of capital or CAPM.
E.g. when r = 0.05:
- DPV = V1/(1+r) + V2/(1+r)2 = 1,100/1.05 + 1,210/1.052 = 2,145.12
- NPV = 2,145.12 – 2,000 > 0
Intern gebruik
, Internal Rate of Return (IRR)
- IRR is also called YTM, it’s an alternative way (to DPV) of evaluating investment projects.
- Compares expected cash flows (CF) and capital costs (KC)
→ Example:
- KC = - $ 2,000 (t = 0)
- CF1 = $ 1,100 (t = 1)
- CF2 = $ 1,210 (t = 2)
- Then: NPV (DPV - cost) = -$2,000 + ($ 1,100)/(1 + r)1 + ($ 1,210)/(1 + r)2
- IRR: $2,000 = ($ 1,100)/(1 + y)1 + ($ 1,210)/(1 + y)2
* what kind or IRR/YTM (y) will make the DPV equal to the KC
* thus, NPV = 0
* IRR tells you what the return is on average
Graphical Presentation : NPV and the Discount Rate
Thus, IRR makes the NPV equal to zero.
DPV = costs.
Investment Decision OVERGESLAGEN
- Thus, invest in the project if:
* DPV > KC or NPV > 0
* IRR > r
* if DPV = KC or if IRR is just equal the opportunity cost of the fund, then investment project
will just pay back the principal and interest on loan.
- If DPV = KC → IRR = r.
Summary of NPV and IRR OVERGESLAGEN
- NPV and IRR give similar results for independent projects with ‘normal cash flows’.
- For cash flows which change sign more than once, the IRR gives multiple solutions and
cannot be used → use NPV.
* NPV is more robust and flexible
- For mutually exclusive projects use the NPV criterion.
Stocks
For stocks, we often need to calculate the fundamental values.
- Vt=Et[Dt+1/R1+Dt+2/R2+…].
* value of a stock equals the discounted present value of future dividends
- When no systematic returns from tradings: Pt=Vt (with systematic returns?).
Gordon growth model: calculates a stock’s fundamental value by summing its discounted
dividends that grow at a constant rate.
- when dividends (D) grow in a certain rate (g), the value of a stock is equal to: V0 = P0 =
D0(1+g)/(R-g).
* R is the (known) required rate of return and g the expected growth of the dividends
- Shows that the price-dividend ratio: P/D = (1+g)/(R-g), is a constant that’s positively related
to growth of the company and negatively to the cost of capital.
* calculating the P/D of a firm, you can infer how much growth people are expecting from
Intern gebruik
, the firm
* when P/D is very high: can be only sustained when company grows very hard
* thus, when firm doesn’t grow as hard as expected, price drops
Systematic trading returns
Solve by backwards induction: all traders are smart and know the others are smart.
Works ONLY if you know that everyone knows that everyone is smart.
31-1, L2: Utility and Risk Aversion
Contents:
- Introduction to utility theory.
- Relative and absolute risk aversion.
- Different forms of utility functions.
- Empirical evidence.
- How useful are the general findings?
* equity premium puzzle
* risk free rate puzzle
Introduction
- Many different investment opportunities with different risk – return characteristics.
- Things will be much simpler if investors are risk neutral.
- General assumption in financial market: ‘people like returns, dislike risk’.
- Preferences of investors (like more to less).
Risk Premium and Risk Aversion
- Risk free rate of return: rate of return which can be earned with certainty (i.e σ = 0).
* e.g a 3 months T-bill
* asset with no risk still earns a return due to time preference
- Risk premium: expected return in excess of the risk free rate (i.e. ERp – rf).
* proportional to the risk people perceive
- Risk aversion: measures the reluctance by investors to accept (more) risk.
* ‘high number’: risk averse
* ‘low number’: less risk averse
→ Example:
- ERp - rf = 0.005 A σ2p
* expected return depends on risk attitude (A) times riskiness of
the portfolio (σ2p)
* thus, more risk averse, you require higher risk premium
- A = (ERp - rf) / (0.005 σ2p)
- SR = (ERp - rf) / σ2p
Indifference curve of this particular preference:
- When σ increases, you require higher return to be indifferent between the two assets.
* non-linear (σ2p): the larger it gets, the more additional higher return you want
Intern gebruik
