🙋 Student Q&A (Lecture 10)

Click here to learn about timestamps and my process for answering questions. Section agendas can be found here. Email office hour questions to rob.mgmte2000@gmail.com . PS1Q2=“Question 2 of Problem Set 1”

📅 Questions covered Saturday, Apr 19

🕣 4:46pm
❔ Imagine you are evaluating a zero coupon bond. With the zero coupon bond, you will receive $1.3 million in five years. What is the fair price of this bond? If you don’t buy this bond, you will invest in a “default investment” that will earn 10%.

To answer this we ask: How much you would need to invest in your “default investment” to get the $1.3M that this zero coupon bond will give you?

I solved this question using $P_{zcb} = \frac{1.3M}{(1.1)^5}$. I would like to know if this is ok as I did not use the formula $P_B x (1.1)^5$. Will I get into trouble later on if I use the formula $P_{zcb} = \frac{1.3M}{(1.1)^5}$ instead of $P_B x (1.1)^5$ to solve for “default investment”?

✔ This is good!

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❔ I was just wondering when you have for example $P_c = \frac{\$23}{10\%} = \$230$ why is the answer not the same for $\frac{\$23}{1.1} = \$20.91$. Isn’t 1.1 the same as 10% ?

✔ Consoles are different the formula for a regular bond (ie regular PV) assumes that you only get one payment of, for example, $23.

$$PV = \$23/(1+10\%)^T$$

In a consol, however, you receive and infinte string of payments. Therefore, we need a different formula. The PV/PB will be much higher because you get an infinite steam of payments. The followin gwill give you a much larger number:

$$PV = \$23/10\%$$

📅 Questions covered Tuesday, Apr 22

🕣 8:17pm
❔ I am a bit confused as to how you solved the following i.e. 108 / 100 = 8%:

Suppose I borrow x today and pay back y in 1 year. What is the effective interest rate on the loan?

i = y /x -1 = y - x / x = 108 - 100 / 100 = 8% = new - old / old

The problem/question is from Lecture 6 —> Example IRR problems —> 3rd example.

✔ This was a shortcut formula. Don’t worry about it.

You would solve it using an IRR computations.

PV Inflows = x PV Outflows = y/(1+i)

IRR: PV Inflows = PV Outflows x = y/(1+i) 1+i = y/x i = y/x - 1 = 108/100 - 1 = 1.08 -1 = .08 = 8% i = y/x - 1 = (y-x)/x = (new - old)/old

🕣 8:21pm
❔ In question it gives E(ri) = 18%. I have not seen E(ri) in the lecture or your notes. My question is if E(ri) is the same as E(rs)?

✔ Yes.

If there are many interest rates, economists will refer to them as r1, r2, r3, etc. If we want to refer to one of those interest rates, but don’t know which one, we write ri. That’s the spirit in which he wrote ri. It just means the return for an arbitrary stock.

Likewise, rs just means the return for an arbitrary stock.

🕣 8:59pm
❔ Are 3c and 4d intertwined together.

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🕣 8:01pm
❔ How does Malkiel disprove the argument that arbitrage is risky?

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🕣 8:01pm
❔ Question 13 doesn’t specify that it is about the CAPM. Can I assume the CAPM and it’s equation hold when answering that question?

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🕣 8:02pm
❔ How is Shleifer definition of arbitrage different from Malkiel?

✔ discussed on video. Basically, they both believe that arbitrageurs are people who attempt to make money by finding security mispricings. Such people bring securities prices to their fundamental values.

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❔ This is a side question to the “side quest,” but I think it relates to how we measure returns over time. On the E*TRADE screen (just as with similar layouts on other broker accounts) it lists the “Total Gain/Loss %” which shows how much your account has grown or shrunk over its lifetime. We’re often told that a good return for, say, a retirement account is 8% per year. If we’re looking at the Total % over an account’s lifetime and trying to see how much it’s grown per year, is that a straight division (total growth/# of years) or is it a more complex calculation due to compounding?

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If my investments have a x% return over n years, then my annual return (CAGR) ((1+x%)^(1/n)-1)*100