EC3333: Financial Economics I
AY2013/2014, Semester 1, Lecturer: Lim Boon Tiong
Course Coverage:
1. Financial Markets
2. Risk & Returns
3. Markowitz Portfolio Selection Model
4. Capital Asset Pricing Model (CAPM)
5. Bonds & Term Structure of Interest Rates
6. Bond Portfolio
7. Equity Valuation Model
8. Options, Futures and Swaps
This module is a mixture of financial mathematics and application. The first half focus on deriving CAPM, where all assets are assumed to differ only in risk and returns. Markowitz Portfolio Selection Model will be used to derived the most optimal risky portfolio, and it is necessary that this portfolio lies on both the Capital Allocation Line(CAL) and the efficient frontier of portfolio combinations. Mathematically, setting the first derivative of the efficient frontier portfolio to be equal to that of the CAL will yield the maximum Sharpe Ratio, which offers the best reward-to-volatility ratio. Graphically, this portfolio is represented by the point where CAL is tangent to the efficient frontier of portfolios. All rational investors should invest in this risky portfolio regardless of risk aversion. However, the amount allocated between the risky portfolio and the risk-free asset will depend on their risk aversions as determined by their utility functions.
CAPM is the financial model underlying all modern portfolio theories. Unlike Markowitz's model, this model assume that the assets in the market have a specific share in the market, formulating a fixed Capital Market Line(CML), and then mathematically search for the most optimal risky portfolio. One of CAPM's implication, the One Fund Theorem states that all investors will hold the same minimum-variance efficient portfolio, which is a percentage of the market portfolio, and the invest the remaining sum in risk-free assets. Several other important concepts are alpha, beta and systematic risk. Alpha determines if a particular asset is underpriced or overpriced, with positive alpha implying an underpriced asset. Beta, also known as the correlated relative volatility, measures the volatility of the portfolio or asset against the market portfolio. The market portfolio has a beta of 1, and hence any portfolio/asset with beta more or less than 1 implies a higher or lower volatility respectively. If the beta is negative or zero, it implies that the portfolio/asset either moves in the opposite direction of the market portfolio, or is uncorrelated to the market portfolio.
The second half of the course focuses on the individual assets. Bonds, or debt instruments, are generally risk-free in the context of the module, with some exposure to credit risks and junk bonds. Common risk-free bonds are T-bills, T-notes and T-bonds, which differs only in their maturities. Other than bond pricing, certain important properties of the bonds include bond duration and convexity, which are useful in immunizing bond portfolios. Yield is also another important feature of bonds, measuring the bond returns and hence the discounting of face values. Term structure of interest rates will cover the yield-maturity relationship, as well as the relationship between spot and forward rates.
Lastly, bond portfolios will involve calculations on portfolio returns and duration, as well as portfolio immunization against credit risk.
Equity is a relatively smaller topic on stocks, and how stocks of companies are valued. Some interesting notions in this segment is the plow-back ratio and how it affects dividends and hence the value of the stock. Some present value analysis is required but it is one of the easiest topic in the module.
Options, futures and swaps are financial derivatives that rely highly on computational mathematics. Options will be covered extensively using
Binomial Option Pricing Model, with a brief introduction of the famous Black-Scholes Option Pricing Model; whereas futures will be covered mainly within the context of futures-forward equivalence, as well as hedging techniques using futures. Some specific futures contract covered are interest rate futures, currency futures and index futures. Swaps are essentially a contract of multiple futures over a swap tenor, used by two counterparties to utilize each other's advantage in a specific market. Common swaps are commodity swaps, interest rate swaps and currency swaps.
This module is rather computational, requiring a lot of calculations using series summation and discounting. It's one of the rare economic modules where decimal places are actually important because most answers never looked nice after discounting. This module does not require too much mathematical knowledge, but proficiency with calculators is a must. Otherwise, you will lose out in calculation speed in final exams, which may or may not make a difference. In this particular semester, exams were literally tutorial-standard with only 2 out of 7 questions that were new. I got overconfident and left at the 1 hour mark, only to realize I did not complete the paper in its entirety. Always check and double check computational papers because you probably left out a decimal place somewhere or forget to solve for the answers numerically. Caution and calculator proficiency is what it takes to score well in this module.
Workload: Moderate
Difficulty: Moderate
Grade: B+
Course Coverage:
1. Financial Markets
2. Risk & Returns
3. Markowitz Portfolio Selection Model
4. Capital Asset Pricing Model (CAPM)
5. Bonds & Term Structure of Interest Rates
6. Bond Portfolio
7. Equity Valuation Model
8. Options, Futures and Swaps
This module is a mixture of financial mathematics and application. The first half focus on deriving CAPM, where all assets are assumed to differ only in risk and returns. Markowitz Portfolio Selection Model will be used to derived the most optimal risky portfolio, and it is necessary that this portfolio lies on both the Capital Allocation Line(CAL) and the efficient frontier of portfolio combinations. Mathematically, setting the first derivative of the efficient frontier portfolio to be equal to that of the CAL will yield the maximum Sharpe Ratio, which offers the best reward-to-volatility ratio. Graphically, this portfolio is represented by the point where CAL is tangent to the efficient frontier of portfolios. All rational investors should invest in this risky portfolio regardless of risk aversion. However, the amount allocated between the risky portfolio and the risk-free asset will depend on their risk aversions as determined by their utility functions.
CAPM is the financial model underlying all modern portfolio theories. Unlike Markowitz's model, this model assume that the assets in the market have a specific share in the market, formulating a fixed Capital Market Line(CML), and then mathematically search for the most optimal risky portfolio. One of CAPM's implication, the One Fund Theorem states that all investors will hold the same minimum-variance efficient portfolio, which is a percentage of the market portfolio, and the invest the remaining sum in risk-free assets. Several other important concepts are alpha, beta and systematic risk. Alpha determines if a particular asset is underpriced or overpriced, with positive alpha implying an underpriced asset. Beta, also known as the correlated relative volatility, measures the volatility of the portfolio or asset against the market portfolio. The market portfolio has a beta of 1, and hence any portfolio/asset with beta more or less than 1 implies a higher or lower volatility respectively. If the beta is negative or zero, it implies that the portfolio/asset either moves in the opposite direction of the market portfolio, or is uncorrelated to the market portfolio.
The second half of the course focuses on the individual assets. Bonds, or debt instruments, are generally risk-free in the context of the module, with some exposure to credit risks and junk bonds. Common risk-free bonds are T-bills, T-notes and T-bonds, which differs only in their maturities. Other than bond pricing, certain important properties of the bonds include bond duration and convexity, which are useful in immunizing bond portfolios. Yield is also another important feature of bonds, measuring the bond returns and hence the discounting of face values. Term structure of interest rates will cover the yield-maturity relationship, as well as the relationship between spot and forward rates.
Lastly, bond portfolios will involve calculations on portfolio returns and duration, as well as portfolio immunization against credit risk.
Equity is a relatively smaller topic on stocks, and how stocks of companies are valued. Some interesting notions in this segment is the plow-back ratio and how it affects dividends and hence the value of the stock. Some present value analysis is required but it is one of the easiest topic in the module.
Options, futures and swaps are financial derivatives that rely highly on computational mathematics. Options will be covered extensively using
Binomial Option Pricing Model, with a brief introduction of the famous Black-Scholes Option Pricing Model; whereas futures will be covered mainly within the context of futures-forward equivalence, as well as hedging techniques using futures. Some specific futures contract covered are interest rate futures, currency futures and index futures. Swaps are essentially a contract of multiple futures over a swap tenor, used by two counterparties to utilize each other's advantage in a specific market. Common swaps are commodity swaps, interest rate swaps and currency swaps.
This module is rather computational, requiring a lot of calculations using series summation and discounting. It's one of the rare economic modules where decimal places are actually important because most answers never looked nice after discounting. This module does not require too much mathematical knowledge, but proficiency with calculators is a must. Otherwise, you will lose out in calculation speed in final exams, which may or may not make a difference. In this particular semester, exams were literally tutorial-standard with only 2 out of 7 questions that were new. I got overconfident and left at the 1 hour mark, only to realize I did not complete the paper in its entirety. Always check and double check computational papers because you probably left out a decimal place somewhere or forget to solve for the answers numerically. Caution and calculator proficiency is what it takes to score well in this module.
Workload: Moderate
Difficulty: Moderate
Grade: B+