Investment Analysis: HW week 8 Solutions
1. Over the past month, TSLA made 14% and GOOG made -12%. The risk free rate was 1% (EMR). How much would you have today if you had invested the following amounts one month ago? Start by working out the portfolio return
(a) $2000 in GOOG, $2000 in TSLA You have invested $4000 in total. The portfolio weights are:
wARA+ wR = 0.5(-12)+(0.5)(14) = 1%. For every dollar you invested in the portfolio, you made 1% - that $1 turned into $1.01. You invested $4000, so you are left with 4000 times that, so 4000(1.01) = 4040. Here's another way you could have done it: you know that from your investment with GOOG, you lost 12%, so your loss is 2000*(12)=240. On your investment in TSLA you made 14%, so your gain is 2000*14=280. In total you made 40, on an investment of 4000, a gain of 1%, leaving you with 4040.
(b) Invest $2000 of your own money in this way: short $2000 in TSLA, $1000 invested in a bank account, the rest in GOOG. You have invested $2000 in total ("your own money"). The amount you "put into" TSLA is -2000, since you didn't put any money in, you got money out.
2000 of your own money, you invested 1000 in the bank account, that means you have 3000 left to put into GOOG. The portfolio weights are:
Check that the weights sum to 1. So your portfolio return is Rp = wARA+wRB+ wcRc = 1.5(-12)+(-1)(14)+ (0.5)(1) = -31.5%. For every dollar you invested in the portfolio, you lost 31.5% - that $1 turned into $1-.315=$.685. You invested $2000, so you are left with 2000 times that, so 2000(.685) = 1370.
(c) Borrow $5000,and buy $10000 worth of TSLA The total invested is $5000: you borrowed an extra 5000 and put 10000 into TSLA.
the weights sum to 1.
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So your portfolio return is 2(14)+(-1)*(1) = 27%. You are left with 5000(1.27) = 6350.
(d) Borrow $5000, and buy $10000 worth of GOOG The weights are the same as in the previous problem, so your portfolio return is 2(-12) + (-1) * (1) = --25%. You are left with 5000(1 + (-.25)) = 3750. (e) What are your thoughts about "using leverage", i.e., borrowing to make an in- vestment, based on the last two scenarios? If you use leverage, you can "win big", as when you borrowed and invested in TSLA which did well, but you can also "lose big", as when you borrowed and invested in GOOG which did terribly. Leverage means that you magnify your return on the upside as well as the downside: you create volatility.
2. You are given the following information: Stock Expected return (in %) (standard deviation) (in %) A 10 10 B 5 5 The covariance between these returns is 16%2
(a) What is the correlation between A and B? The formula for correlation between two assets is
Cov(A,B) Correl(A,B)= SDASDB
So here
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