Investments GRA6534 - Lecture 1 Giovanni Pagliardi Welcome! • Instructor • Giovanni Pagliardi - PhD, ESSEC Business School Paris • Email: giovanni.pagliardi@bi.no • Office hours: Thursday 10.00-12.00 or by appointment • This course • 12 lectures • 2/3 synchronous, 1/3 asynchronous • • • • • Two events (BI Talks) in addition to the 12 lectures: Nicolai Tangen and Kjerstin Braathen Pre-recorded videos. To be watched after class Two take-home projects in groups Digital drop-in sessions Non-mandatory sets of individual homework assignments Determination of final course grade • Work requirement: Bloomberg Market Concept • All students must get the BMC certification before October 4th at 23.59 • To validate the BMC one must get at least 50% of correct answers in the sections of the BMC considered mandatory to receive the Bloomberg certificate • Careful! If you forget to complete it, BI will not allow you to take the final exam • Mid-term test (counts 30%) • On November 7th • It includes two parts: • Two take-home projects to be done in groups of 4-5 students, during the semester • One 24-hour, take-home multiple choice test to be done individually • All students must upload the PDFs of the two projects in Wiseflow when submitting their answers to the multiple choice • The multiple choice will cover theory questions or short exercises related to the projects • You will receive a letter grade for the midterm test as an average of the projects and the test Determination of final course grade • Final written (counts 70%) • It includes three parts: • Multiple choice • Exercises • True/False with explanation of the answer in maximum 5 lines • You will receive a letter grade from the final exam as well • The final course grade is determined as a weighted average of the two letter grades from the midterm and final exams, conditional on the validation of the BMC • Example 1: The student receives A in the 70% component and B in the 30%. Grade: A • Example 2: The student receives B in the 70% component and A in the 30%. Grade: B Contents – Lecture 1 1. Overview of the course 2. Pricing different investments 3. Risk – expected return trade-off Example with lotteries 4. Two ways of pricing 1. OVERVIEW OF THE COURSE β Four different types of investments covered in this course: a b BONDS • Bond pricing. • The term structure of EQUITY related c HOUSING • • interest rates. assignment will come FUNDS (Alternative investments) Difference between The most important question to be answered is: hedge funds, mutual Can returns be predicted? funds, and closed-end funds. β After this point, the first computer d • There is a strong similarity between equity returns For each type of investment, the pricing is done in the same way. and housing returns. out. 6/13 2. PRICING OF DIFFERENT INVESTMENTS • There are two essential approaches to price any kind of investments: 1 • RISK-BASED EXPLANATION Entirely based on the rationality of the investors, 2 • BEHAVIORAL EXPLANATION Tells you that investors are not necessarily always rational. i.e., the investors can process all the info they have well, and in the end, they base their For this course, we will start with the assumption that investors are rational and will see how to price the assets to reflect their risk. • There are other factors, like: decision on the trade-off between risk and — Overreaction expected returns. — Optimism Example 1: Investors’ overreactions after news. Example 2: CUBA fund (2014) Example: It’s 2011 and you have a Norwegian government bond and a Greek government bond. Which one would you prefer? Hint: first look at the risk, then set the price. 7/13 3. RISK – EXPECTED RETURN TRADE – OFF • The expected return of an asset is the expected gain divided by the price: πΌπ = πΌπ‘ πΊπππ ππ‘ = πΌπ‘ ππ‘+1 −ππ‘ ππ‘ = πΌπ‘ ππ‘+1 ππ‘ −1 If we rearrange: 1+πΌ π = πΌπ‘ ππ‘+1 ππ‘ Remember our goal: To find the price of our investment, so you can decide to buy or sell. 9/13 If we solve for Pt, we get the standard pricing formula: ππ‘ = πΌπ‘ ππ‘+1 1+πΌ π β The asset’s price today is the expected value of my cash flows tomorrow, discounted at a certain interest rate. • If you want to find the price of an investment, you need to compute two quantities: πΌπ‘ ππ‘+1 and 1 + πΌ π . • πΌπ‘ ππ‘+1 is the expectation of a future price (i.e., what would be the cash flow tomorrow?). β You dont’t take into account any uncertainty around that expectation. Then, where are you taking into account the risk in your computation? β At the DENOMINATOR! ⇒ Risk must be incorporated in the expected returns (πΌ π ). 10/13 Expected returns are only determined by risk! EXAMPLE WITH LOTTERIES • Let’s try to show that there must be a relationship through which expected returns are only determined by risk. • Let’s suppose that we have three lotteries: Lottery Pay-off Probability of pay-off Expected pay-off (πΌ[π·πππππ]) A $100 100% $100 B $0 or $200 50% $100 or $300 50% C $100 50% $200 50% 11/13 Question: Between B and C, which lottery would you prefer? Question: Which lottery is riskier? Remember that: ππ‘ = πΌπ‘ ππ‘+1 1+πΌ π Price lottery A: Price lottery B: 100 ππ‘ = 1 + πΌ[π] 100 ππ‘ = 1 + ππ Let’s assume investors are willing to pay $80 for Where ππ is the risk-free rate. every $100 they are promised. Therefore, lottery A is a riskless asset. ⇒ ππ‘ = $80 100 ⇒ 80 = 1+πΌ[π] ⇒πΌπ = 12/13 100 − 80 1 = ππ% Question: Between lottery A and B, which one would you prefer? Note: πΌ ππ΅ > πΌ[ππ΄ ] A statement on expected returns is always a statement on prices When πΌ π increase (decrease) ⇒ prices decrease (increase) • We are trying to explain what is driving investors’ expectations of future returns. Expected returns ≠ Realized returns This course will try to model expected returns 13/13 Price lottery C: • Let’s assume that standard deviation (sd) is our measure of risk. • Note that π ππ΅ = π ππΆ • If B and C have the same measure of risk and risk is the only thing that drives expected returns, ⇒ Lottery B and C have the same ex-ante expected returns in equilibrium. • If you are willing to pay $80 to get $100 (lottery B), how much are you willing to pay in order to get $200? Answer: $160 = ππΆ 160 = 200 1 + πΌ[ππΆ ] βΉ πΌ ππΆ = 200 −1 160 βΉ πΌ ππΆ = 25% Conclusion: You should be indifferent between lottery B and C. β They have the same risk and the same expected return. 14/13 4. TWO WAYS OF PRICING (for any investment) • Remember the standard way of pricing an asset: ππ‘ = A B Incorporate risk in the discount rate (denominator) ππ‘ = πΌπ‘ πΆπΉπ‘+1 1+πΌ π • π×πΆπΉπ‘+1,1 + 1−π ×πΆπΉπ‘+1,2 1+ππ +π πππΎπ +π ππππ΅ +β― Incorporate risk in the numerator In this approach, we need to adjust the expectation with a different probability measure to account for risk. Risk premium • CAPM You discount at a risk-free rate. So you have: ππ‘ = Multifactor models: You consider all the possible risks π×πΆπΉπ‘+1,1 + 1−π ×πΆπΉπ‘+1,2 1+ππ that might affect your price. Where π is the risk-neutral probability measure. Caveat: You need to estimate them and not all of them will be priced by the market. 15/13 “Annuities and perpetuities” • Did you know there is a trick to derive the Video 1 Video 2 Video 3 Video 4 Video 5 Video 6 formulas of the annuities and perpetuities without learning them by heart? β’ To know how, watch the videos! Test it on your own • How would you compute the present value (t=0) of a perpetuity that starts in the future? • Would you be able to derive the formula for the present value of a growing perpetuity? 16/13 Hw1: Ex 1 LECTURE 1 – Annuity: geometric series – Annuity: final formula – Annuity due extension - Annuity generalization – Perpetuity formula - Perpetuity due extension
