Homework 1 Q&A FINA 6226 spring 2024

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Feb 20, 2024

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Homework 1 FINA 6226: The questions are primarily for currency Forwards/Futures/ETFs, so you can practice calculating returns, and understanding the risk. Answers are below. 1. The following question is aimed at understanding the returns and risks of an Equity Long/short fund. We significantly reduce the reality to make our points in a simple fashion. First we assume that we have a short enough time period such that the cost of borrowing the stock is insignificant (we are also leaving out shorting stocks with high stock borrowing costs). Second, we assume that the period is short enough that the interest earned on the cash received from the short position is insignificant. Third, we assume that no additional cash is required to hold the position (there usually is some, and quite a lot if we have a lot of leverage). Fourth, if there is a lot of leverage, there are borrowing costs. We assume this away as well. Assume that we have 1 million USD under management (AUM). We use it all to buy 20,000 shares of Bhatti at 50 dollars per share. We also short 25,000 shares of Barnes stock at 40 dollars per share. What are our original gross and net dollar exposures? Assume Bhatti stock falls to 47 dollars per share and Barnes stock falls to 36 per share? What is the gain or loss on the position? What is the fund’s holding period return? If we do not rebalance our positions, what are the new gross and net exposures? Gross Dollar exposure is Long exposure plus the short exposure divided by the NAV. This takes into account that you might be wrong on both positions. 1 million plus 1 million divided by 1 million equals 200%. (1+1)/1 x 100%. The net dollar exposure is 0%= (1-1)/1. If the betas are the same then we are Beta market neutral as well. Our return is the net gain or loss divided by the initial NAV. We lose 60,000 dollars on Bhatti stock (20,000 shares) x (50-47). We gain 100,000 on Barnes stock (25,000 shares) x (40-36). The net gain is 40,000 dollars which is 4% on the NAV (1 million dollars). The new NAV is thus 1,040,000 ( 1m + 40,000), as we made more on our Barnes short position as we lost on our Bhatti Long position. The new value of the long position is (20,000 shares) x (47 dollars per share) = 940,000 dollars. The

new value of the short position is (25,000 shares) x (36 dollars per share) = 900,000 dollars. The aggregate exposure has thus become (940,000 + 900,000)/ 1,040,000 x 100%= 176.92%. The net exposure has become (940,000 – 900,000)/1,040,000 x 100% = 3.846%. We are now very very slightly long biased (effectively market dollar neural), and our gross leverage has declined from 200% to 176.92% (2x1 to 1.7692x1). 2. The Professor Selender firm has 100M AUM. The firm is Long 80 million of stock A and short 80 million of stock B. What are the gross and net dollar exposures and leverage? If the Beta of the portfolio is .2, what does that imply concerning the relative Betas of stock A and stock B? What if the portfolio Beta is zero? What if the portfolio Beta is -.2? The Flowery Firm also has 100 million under management, but is long 100 million stock A and short 40 million of Stock B. What is the gross and net dollar exposure and leverage? What does a portfolio Beta of .6 imply concerning the relative Betas of Stock A and Stock B? The selender firm has a dollar gross exposure of 160 million and a net dollar exposure of zero. The gross leverage is 1.6 to 1. Since the dollar exposures are the same for stock A and Stock B, they will have a beta of zero if the Beta of stock A and Stock B are equal. If the Beta of stock A is greater than the Beta of stock B, then the Beta of the portfolio will be positive. The portfolio Beta will be negative if vice-versa is true. The Flowery firm has 140 million gross dollar exposure and 60 million net dollar exposure. Her gross leverage is 1.4 to 1. If the portfolio Beta is .6 then it is approximately true that Stock A and Stock B have the same Beta and it is 1, Note the net dollar exposure is 60 million and she has 100 million under management. 3. Can an industry be in general a good buy in one country and not in another? Explain  Industries can be doing well in one country and poorly in another. There are both global and local industry effects. An industry in country A may be doing poorly because most of the sales are local and that country is going through tough economic times. Alternatively, the industry could be focused on exports but to country B which is performing “gangbusters”.

Example: Japanese car companies export very little to Europe, as there are voluntary limits on Japanese cars being sold in Europe. But the Japanese car companies export much more to the U.S., and thus are affected more by the U.S. economy. Of course, there is a positive correlation between the U.S. and European economies. 4. What is the main reason that long/short equity hedge funds have performance problems during liquidity crunches (2008, for example)?  There is a tendency for Long/short equity funds to be long the more illiquid stocks, and short the more liquid. Most of the time the losses on the Long positions that are due to general market moves are compensated for by the gains on the short positions, if the fund is market beta neutral. During a crisis, the illiquid stocks tend to get hit more percentage-wise when the market is selling off as there are not a lot of bids to hold prices up. Liquid stocks tend to hold up much better, as there are more sizeable bids to help hold up prices. The result is that the short positions do not fully compensate the fund for the losses on the long positions. This means that the correlation with the market approaches 1, although the Beta will be significantly less than 1. For example, if the Beta is .5, then if the market declines 50%, a “market neutral” fund such as discussed will decline 25%. So much for being market neutral! Additionally, a lot of fund of funds employed leverage even if specializing in Long/short equity funds. Loses could thus be much greater than 25%. 5. What are the advantages of evaluating a Country/Industry Matrix, instead of using the “standard” approach. The standard approach is to first pick which Countries we would like to go long and which Countries we would like to go short. We then pick which Industries within the Countries that we are long and we pick which Industries to go short within the Countries that are short.  If I pick countries to go long in, and countries to go short in, I immediately constrain my degrees of freedom. I might; for example, leave out a moderately performing country, that just happens to have a really top notch industry, or an inferior industry. I would miss a chance to go long or short. I can even have cases in which a great country has an industry that is worth shorting, or a horrible country that happens to have one

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industry that is awesome, due to where its exports go. Of course, by approaching the analysis this way, we have a lot more data to deal with, and this could add complications. Also many managers have country specialists that can go long one industry in a country and short another industry in the same Country. Let’s go one step further, a country expert could pick a stock in an industry and go long. The manager can simultaneously short a stock in the same industry and country. An example is as follows: we could go long Toyota and short Honda (we focus on Japan). Is it more interesting to go long General Motors and short Toyota (or vice-versa)? This kind of trade is left out if the traditional approach is used. 6. What is the main disadvantage to a global long/short hedge fund versus a domestic long/short fund?  An international portfolio will have an additional risk--- currency risk. Now currencies may also correlate with stock performance, which will make decisions about hedging more difficult. For example the 2013 depreciation of the Japanese Yen, helped the Japanese Stock Markets, as the markets were assuming that exports will blossom again. So, while JPY depreciation hurts us in direct currency translation risk, it also helps us get a better Japanese yen based return before translating back to U.S. dollars. THE EFFECTS COUNTER EACH OTHER! Do we under, or over- hedge? Of course, the extreme case of under-hedging is not hedging at all. 7. We have 100 million AUD assets under management (AUM). We desire to take advantage of the AUDJPY carry trade. AUDJPY is quoted as JPY per AUD. Spot is bid=80.00, ask=80.10. 1 year Forward Points bid=-152, ask=-150. Why are the forward points negative? We buy 200 million AUD 1-year forward, for AUD. Note we are levered, as we are buying 200 million AUD and our AUM is 100 million AUD. 1-year from now if the AUDJPY spot rate is bid =85.00, and ask =85.10. What was our return on the trade?  Start off by calculating the forward rate for a bought forward as you are buying AUD forward/selling JPY forward. Use the current spot ask and the forward point ask; and you get the forward rate ask. So we take 80.10 and subtract 1.50. The forward points are -150.00. The result is 78.60=(80.10 – 1.50). This means that you bought 200million AUD with JPY at an exchange rate of 78.60 JPY per AUD and sell the AUD at the new spot rate bid of 85.00 JPY per AUD. We would like to put

this gain or loss back into AUD and divide by the AUM of 100million USD in order to calculate the return on the trade. So buy the 200 Million AUD with JPY at the forward rate of 78.60 and then sell the AUD for JPY at the new spot rate of 85.00. We buy 200 AUD , selling 15.72 Billion JPY. We, then sell the 200 AUD at the new spot rate of 85 .00 AUD per JPY. So we receive 17.00 Billion JPY. We have a net gain of 1.28 Billion JPY. In AUD terms at the new spot rate we divided by 85.10 AUD per JPY. This results in 15.04 million AUD. If we divide by 100 million AUD, we get a return of 15.04%. 8. Assume we have 1 million USD under management, and we buy 8 GBP June futures contracts. Note one contract has a notional amount of 62,500GBP. If the futures price is 1.48 today and in two days is 1.46, what do we win or lose and what is the return on the 1 million under management?  GBP futures contracts are of 62,500 GBP. 8 contracts is a notional amount of 500,000GBP. Futures are marked to market every day. So over 2 days your result is (1.46-1.48) X 500,000 GBP = -10,000 USD. So you lost 10,000 USD, which is a 1% loss over the 2 days. Note GBPUSD moved by more than 1%, but the notional size of the trading position is 1 million USD. 500,000 notional GBP is less than 1million USD. 9. We have 300,000USD under management and we want an equally weighted notionally aggregated 3.0X levered carry trade, and we are interested in three currencies: AUD(sell), GBP(sell), and BRL (Buy Brazilian Real). How many futures contracts do we buy/sell of each? Also, if I dropped BRL and am interested in JPY instead; do I buy or sell JPY? How many contracts? The JPY Futures contract has a notional amount of 12.5 M JPY. The latest prices can be found on the CME Group website. Assume AUDUSD=.80, BRLUSD=.27, GBPUSD=1.35, JPYUSD= .0090.  If I have 300,000USD under management and I want aggregate 3 x leverage, than I need a total notional amount of 900,000 USD. If I desire to be equally weighted notionally, than I want 300,000 USD equivalent notional amount for each AUD, GBP, and BRL. We will need to look at futures prices to determine what the USD equivalent is. Assuming the futures prices from above; we can determine how many contracts we will need of each. We take 300,000 USD for each and convert to the foreign currency equivalent then we divide by the notional on the

foreign currency futures contract to get the approximate number of contracts. Assuming AUDUSD October futures are .80; we would take 300,000 USD and divide by .80 to get the AUD notional needed, which is 375,000.00 AUD. Since an AUD futures contact has a notional of 100,000 AUD, your approximate number of contracts is 4. For GBP, if the futures are 1.35 USD per GBP then we need 222,222.00 GBP. Since a GBP futures contract has a notional of 62,500 GBP, we would need 4 contracts (rounding up from 3.55). In the case of BRL (Brazilian real) the futures are approximately .27. So we would need 1,111,111.11 BRL. The contract notional is 100,000 BRL, so we would have 11 contracts. If I want to utilize JPY futures, we would need to sell JPY futures, as the USD has the higher interest rate. So how many contracts would we sell? The futures price is approximately .0090 USD per JPY. So we need 33.333333 Million JPY. Each contract has a 12.5 million Yen notional amount, and thus we are closest to using 2 or 3 contracts. If we round up from 2.67, we end up with 3 contracts. 10. Cross-currency carry trade is AUDJPY. Our portfolio is 100 million USD. We buy 50 million AUD forward, selling JPY. The 3- month forward is at 90 AUDJPY. The 3-month forward for AUDUSD is .80 and the 3-month forward for USDJPY is 112.50. In 3-months time, AUDJPY spot is 100; and USDJPY spot is 100, and AUDUSD spot is 1.00. Note AUDJPY should be AUDUSD X USDJPY. The numbers must work! Note, you have additional risk due to the fact that your gain or loss is not in USD. So what is our return? Did the cross-currency risk affect the return in a significant way?  The purpose of this question is for you to practice calculating returns on a cross-currency carry trade. The complication is that your base currency is different from the currency pairs involved in the carry trade. We can use any AUD notional we want in order to practice. Assuming 50 million AUD, we buy 50 million AUD forward against JPY at 90 AUDJPY. In three months time, AUDJPY is 100. The gain can be calculated in AUD or JPY. Either way, we need to translate back to USD, and then divide by 100m USD (AUM). The gain is as follows: (100-90) x 50 M equals 500 M JPY. The JPY has to be translated back to USD at the new spot rate for USDJPY, which is 100. We divide 500 M by 100 to get the USD equivalent, and we get a 5 million USD

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gain. We thus earned 5% return on our 100 million USD. Note, the AUDUSD risk is secondary, while the primary risk is AUDJPY. 11. If I have 1,000,000 USD under management, and I want to have the same notional amount in USD terms in BRL, and CNY; and I want to use ETFs/ETNs, what can I do? Assume BZF=16.27 and CNY= 43.81.  This is very straight forward. Ideally you invest 500,000 usd in the BRL ETF (un-leveraged version), and 500,000usd in CNY ETF (un-leveraged). However, given the price of the ETF, we will not get 500,000usd exactly. Also note, we have to invest 1 million total or less as that is all the cash we have. ETFs are non-zero investments. Well it is very easy to Google and find BRL and CNY ETFs/ETNs. We can use BZF and CNY as our ETFs/ETNs. It is trivial to look up ETFs. If you Google (FX ETFS LIST), you will get lots of sites. O.K. what are BZF and CNY trading at? Assume BZW=16.37 and CNY=43.81. WE need 30,544 shares of BZF and 11,413 shares of CNY. 12. We have 1 million USD under management, and we want to use ETF’s to take advantage of the USDJPY carry trade. We want to be unlevered; but the only inverse JPY ETF we can buy is 2x leverage (not un-levered). What do we do? How much do we invest in the 2x inverse ETF?  If we only can buy an inverse JPY ETF with leverage, then we need to be careful. In the case of YCS, we have an inverse JPY with 2x leverage. If we have 1 million under management and we have only 2 x leverage available, then we reduce our investment in YCS to 500,000USD, and we keep the other 500,000usd in cash, receiving interest. If YCS is trading at 75.00USD, the total shares are approx 6.67 shares(round off to 7). 13. During what regimes would t-bonds not be a good hedge against stock market declines? Think back to the 70’s and early 80’s.  When interest rates rise due to inflationary expectations, both the stock market and the bond market get hit, or at least the stock market return is curtailed by rising rates. Thus long term bonds will not be an effective hedge against the stock market.

You will have to have an asset positively correlated with inflation and/or a component of your portfolio in cash that you can take advantage of rising short term rates. If changes in real rates are the main factor in nominal rate changes (for example, reduced demand for investment) than Bonds are good hedges against stocks. This has been the case through most of the 2008/post-2008 period. Investors are now worried that we are entering a period in which Bonds are no longer a good a good hedge against declining stock markets.

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