# 这是一篇来自美国的关于财务风险管理的经济代写

Problem 1

Futures. Say that on December 16, 2022, you invested \$25,000 in one of the following strategies:

(i) invest 100% in SPY, an ETF that tracks the S&P 500, or

(ii) go long X = 1 or 2 e-mini S&P 500 futures expiring in March 2023. For this strategy, you hold non-margin funds in cash.

For strategy (ii) assume throughout that the initial margin is \$11,660/contract and the maintenance margin is \$10,600/contract.1 Also assume that you buy fractional shares of SPY since \$25,000 won’t buy a whole number of shares.

See the Excel fifile posted on Blackboard for data. E-mini data is from Marketwatch and SPY data is from Yahoo! fifinance. I also fifill in some numbers without formulas that might help you check your work.

(a) (5 points) Find the total return (in %, not in \$) from December 16, 2022 to January 23, 2023 for the SPY strategy in (i). Note: SPY pays dividends. This means the daily (gross) return is given by:

returnt,t+1 =Pricet+1 + dividendt+1pricet .

However, in the excel sheet, I provide the adjusted close, which assumes you reinvest any dividends so that returnt,t+1 =adjusted closet+1/adjusted closet

(b) (5 points) One metric that can assess the riskiness of a position is the Maximum Drawdown. It is computed as follows:

• For each day, compute the running maximum value (i.e. the peak value) of the position from date 0 (when you start the investment) until now (time t):

Mt = max{V0, V1, V2, . . . , Vt}

See the Excel column ”Running Max”.

• The drawdown at time t is how far we are currently below the running maximum:

DDt = (Mt Vt if Mt > V0 otherwise

Note if we are currently above the running maximum, the drawdown is 0. We sometimes write this last formula as max(Mt Vt, 0) or (Mt Vt) +.

See the Excel column ”Drawdown”.

• The maximum drawdown over the life of the investment is then:

MDDT = max{DD1, DD2, . . . , DDT }

Find the maximum draw down over the 1-year investment for the SPY strategy in (i).

(c) (5 points) Find the P&L on the trade for the fifirst day due to marking-to-market when you are buying X = 2 e-minis. Recall:

Mark-to-market P&L = (multiplier) × (Ft+1 Ft) × (number of contracts)

In the Excel fifile, I include the new value of the X = 1 position on the fifirst day. If you add some absolute cell references (\$) you can copy-paste this formula throughout the fifile.

(d) (5 points) We can defifine the leverage ratio of a futures + cash position as:

(Notional Value of Underlying) × (futures multiplier) × (# of contracts)

(amount of cash holdings, including margin)

The numerator gives the total risk exposure in dollar terms. Find the leverage ratio for each futures’ position X = 1 and X = 2.

(e) (5 points) Find the total return (in %) for each of the strategies X = 1 and 2 over the holding period December 16, 2022 to January 23, 2023.

(f) (5 points) Would there be a margin call for X = 2 contracts strategies?

(g) (5 points) For the X = 2 strategy, fifind the maximum drawdown.

Problem 2

(10 points, 5 points each) True or False. State whether the last sentence is true or false. No explanations are necessary; the grade will be based on the answer only.

(i) Suppose you want to bet that the S&P 500 would go down. Rather than shorting the 500 stocks individuals, you could instead short the e-mini contract.