# FAQ
For Final:
Q: And just to confirm, we are allowed to use both sides of a paper for our aid sheet for the exam?
A: Yes.
Q: The final exam is cumulative? Is there a specific weighting on the topics for the final exam, i.e 60% of final exam being tested on material on test 2 until end of course and 40% of topics being test 1 material or 50/50 ?
A: Yes the final is cumulative and I would say around 50% after Test 2, and 25% on the material on Test 1 and on Test 2. Approximately.
Q: What happens to call put prices when interest rate increase?
A: "Call: Higher interest rate means higher call because higher interest rate means in real term you are paying less for the underlying. Put: Higher interest rate means lower put because higher interest rate means in real term you are getting less for the handing in the underlying." In real terms, the amount you pay (for call) or receive (for put) is just the present value of the strike (exercise) price.
Q: What is in the money and out of the money call put?
A: K is the strike (exercise) price, S is the initial stock price. In the money call is when S > K. In the money put is when S < K. Out of the money call is when S < K. Out of the money put is when S > K. At the money call and put are when S = K. Intuitively, in the money means making a profit if exercise now; out of the money means making a loss if exercise now.
Q: Do we need to know the following concept in the exam? More on CAPM Q6C: RRR(reward to risky ratio) Q8C: R-square formula
A: Since they are from the notes. Yes.
Q: When we are asked to calculate the variance of a portfolio constructed from 2 assets(A&B), if we were given both rhoA,B and rhoA,m & rhoB,m, which formula should we use? Should this two formulas have similar result?
A: The first. (The one without beta.) But both will result in the same answer.
Q: Why APT cannot be used to price undiversified portfolios?
A: From Test 2: "Single stocks (or non-diversified portfolios for that matter) carry firm specific risk so at any point in time their departure from the SML might be due to mispricing (abnormal return) or firm specific risk, there is no way to be certain of either. Therefore, we cannot build an arbitrage. Diversified portfolios carry no firm specific risk therefore their departure from SML is definitely mispricing (abnormal return) and can be arbitraged out by creating a synthetic portfolio that falls on the SML."
Q: when we are calculating the delta, how to we calculate the result of the short call? In your videos, you used taught us to use 100*1.1-100=10, but here the professor apparently analyzed the second period and used 100*1.1*1.1*0.75/1.05 =15 as the result. Which one is correct?
A: The question said "one-period call", so it is not clear whether (1) it is a one-period call with the same strike as the two-period call in parts (a) and (b) OR (2) it is the two-period call in parts (a) and (b) that will be liquidated in one period. If the assumption is (1), then my method is correct; otherwise (2), then the professor's solution is correct. On the exam, if the same thing happens, state your assumption clearly and solve the question accordingly. I will either grade the exam this way myself or tell the other TA I said it during my tutorial if she grades that question.
Q: In the binomial model, the risk-neutral probability cannot be more than one?
A: Yes. If there are two, then there will be an arbitrage opportunity. It's the same idea as the risk we cannot have two different risk-free rates.
Q: Everything else similar, An at the money European call is more expensive than an at the money Put.
A: I think I had a video for this question on my web page that explains this better, but briefly: it can be proven using call-put parity. P + S = C + PV(K) implies (given "at the money" meaning K = S) P - C = S - PV(K) = S - PV(S) > 0. Therefore P > C, put is more expensive than C.
Q: Can you email me past exam questions and/or solutions?
A: NO.
Q: I just want to confirm what was said in lecture: there will be nothing on the exam regarding stocks. Is this correct?
A: NO, of course there will be questions on stocks. Most of the questions on the sample and previous exams are about stocks.
Q: Is using Black-Scholes method also required for us to know for the exam?
A: YES, but you only need to know the formula, not its derivation, the greeks, etc.
Q: Can asset return be negative? A problem in the problem set, the expectation of market use the negative return but it uses the absolute value while calculating the risk of the market. eg: E=0.4*(2-1)/1 + 0.6*(0.5-1)/1=0.1, (0.5-1)/1 is negative. But var of the market is: 0.4*(2-1.1)**@2 +0.6*(0.5-1.1)**2, why does it use 0.5 rather than -0.5?
A: Yes. Returns can be negative. (-0.5)^2 = 0.5^2. Squaring a negative number and squaring its absolute value is the same.
Video Recordings: (see note on the bottom of the page)
Sample Final Q1a:
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Sample Final Q1b:
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Sample Final Q1c:
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Sample Final Q1d:
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Sample Final Q1e:
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Sample Final Q1f:
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Sample Final Q2a:
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Sample Final Q2b:
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Sample Final Q2c:
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Sample Final Q3a:
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Sample Final Q3b:
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Sample Final Q3c:
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Sample Final Q4a:
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Sample Final Q4b:
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Sample Final Q5a:
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Sample Final Q5b:
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Sample Final Q5c:
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For Test 2:
Q: The difference between CAL, CML, SML, SCL.
A: CAL is the relationship between risk and return for ONE SPECIFIC ASSET. The asset can be any stock or portfolio.
CML is the CAL for the MARKET (TANGENCY) PORTFOLIO.
SML is the relationship between beta (NOT RISK) and return for ALL ASSETS, including risk free (beta = 0) and market portfolio (beta = 1).
SCL is the relationship between (excess) return for ONE SPECIFIC ASSET and the MARKET PORTFOLIO, used to find beta of that asset.
Q: If the minvar portfolio is risk free (happens when correlation between risky assets A and B is -1) but its return is NOT the same as the risk free rate (borrowing is allowed), what is CAL?
A: CAL is the vertical line along the y-axis above the risk free rate. I said there is NO CAL during the tutorial, you can write that on the exam too. If borrowing is NOT allowed AND risk free rate is higher than the return of the minvar portfolio, then CAL is the line connecting the risk free asset and the risky asset (either A or B) with the higher Sharpe ratio.
Q: How do I calculate covariance AND correlation factor if the question only gives us probability of each 'state of the world' (i.e. very bad, bad, good, ...etc.) and the return for each of the three assets.
A: Covariance of X, Y = E(XY) - E(X)E(Y). Correlation of X, Y = Cov(X, Y) / sqrt(Var(X) Var(Y)). Here, X and Y are random variable of the returns, and E(*) is the expectation.
Q: For Q1a in sample test 1: Is there any typo in this question? I have no idea what does 'slope of sharpe ratio' mean, since the sharpe ratio is a ratio already.
A: I guess the typo is "slope of SML" from the answer, but I am not sure.
Q: First, for Q3b in sample test 1, why do we assume the correlation between asset B and asset C equal to 1? Is it just a routine assumption (i.e. we would keep assuming this in test2) or does the correlation has to be? If so , why is that.
A: No, we didn't assume correlation is 1 and we don't want to assume it on test 2. Without diversification is just the weighted average risk. There is no need to assume any covariance.
Video Recordings: (see note on the bottom of the page)
Sample Test 2 Q1a:
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Sample Test 2 Q1b:
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Sample Test 2 Q1c:
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Sample Test 2 Q1d:
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Sample Test 2 Q1e:
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Sample Test 2 Q1f:
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Sample Test 2 Q2a:
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Sample Test 2 Q2b:
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Sample Test 2 Q2c:
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Sample Test 2 Q3a:
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Sample Test 2 Q3b:
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Sample Test 2 Q3c:
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Sample Test 2 Q3d:
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Sample Test 2 Q4a:
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Sample Test 2 Q4b:
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Sample Test 2 Q4c:
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For Test 1:
Q: Is it also acceptable if I was to create a CF table and realize all the arbitrage profit now(aka, at CF0)? I saw both sample tests just show how to create synthetic forward rate instead of showing the arbitrage profit?
A: I did both versions during the tutorial (profit now and in year two). I prefer realizing the profits now on the exams.
Q: When the question says "the one year treasury bond yields 3%", does it mean that it will pay $100 at maturity, or it will pay $103 at maturity? The answer to part (a) seems to be based on a $100 payment at maturity discounted for a discount rate of 3%?
A: (i) The yield rate is the same as the discount rate for bonds. The coupon rate is the rate that determines what the buyer at the end of each period. (ii) Treasury bond is the same as zero coupon bond, therefore, in this case, coupon rate is zero and yield rate (discount rate) is 3%. (iii) The principal payment is always the same as the face value, so the buyer pays 100 dollars at the end. The equilibrium price is 100 / 1.03.
Q: Why P_5 = (1.5 * 1.05^6) / (0.11-0.05) = 33.50. Shouldn't it be the power of 5 instead of 6?
A: No. According to the annuity formula, year 5 value is dividend at year 6 divided by the interest rate. So the power should be 6.
Q: Why the perpetuity starting at year n is discounted to time 0 using (1 + r)^(n - 1) but NOT / (1 + r)^n?
A: NO! It's only because the formula x / (r - g) discounts a perpetuity starting at year n back to time n - 1. The value at year n (not year n - 1) for a perpetuity starting at year n is x (1 + r) / (r - g). g is the growth rate.
Q: What is the difference between YTM, HPR, IRR etc?
A: They are ALL discount rates, meaning $1 now becomes $1+r in the next period, just different names for different types of financial instruments.
For any specific bond: Yield to Maturity / Internal Rate of Return must be the same in each period (until maturity).
For any specific stock: Required rate of return / Cost of Capital must be the same in each period.
For risk-free bond (T-bills): Spot rate / Forward rate / Short rate can be different in each period.
For risk-free borrowing and lending: Interest rate / Risk-free rate usually the same in each period, but can be different.
For any specific bond or stock: Holding Period Return can be difference in each period.
Q: What is the formula for Dividend yield?
A: (Div Gain) / P0 = (FV5 - P5) / P0 if the stock is sold at year 5.
Q: What's wrong with "Constant stock price iff constant dividend and discount rate"?
A: Also need constant growth rate.
Q: Cheat Sheet?
A: Single-sided and CANNOT be printed or photocopied! You can write / draw whatever you want on it.
Video Recordings: (see note on the bottom of the page)
Sample Test 1 Q1a:
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Sample Test 1 Q1b:
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Sample Test 1 Q1c:
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Sample Test 1 Q1d:
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Sample Test 1 Q1e:
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Sample Test 1 Q2a:
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Sample Test 1 Q2b:
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Sample Test 1 Q2c:
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Sample Test 1 Q2d:
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Sample Test 1 Q3a:
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Sample Test 1 Q3b:
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Sample Test 1 Q4a:
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Sample Test 1 Q4b:
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Sample Test 1 Q4c:
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