Hedge Fund - Derivatives Case Assignment

Derivatives case assignment

1. Estimation of risk factors:

Based on each company's background and specific industry, we estimate the following risk factors as the vital ones influencing the companies' stock return. As for the portfolio which consists of all five, we hold the idea that all the factors that affect these companies will also influence the return of the portfolio. The results are listed below:

Figure 1. Risk Factors Forecasting (Based on company's background)

Company

/Portfolio Background Corn Crude Gold Nikkei S&P 500 Canadian Yen

ABX US Canadian-based Gold Mining Company √ √ √ √

XOM US US-Based Energy Company √ √ √

CAT US US-Based Earth-Moving Equipment Firm √ √

ADM US Corn and Soybean processor √ √ √

6301 JP Japan-Based Earth-Moving Equipment Firm √ √ √

PORTFOLIO Combination of all five stocks √ √ √ √ √ √ √

2. Specify the factors based on weekly data.

To verify the estimation, multiple regressions are used to identify statistically significant risk factors. Firstly, we run the regression for each company's log return with all the seven factors' change rate; secondly, based on our regression output, we delete the insignificant factors; then, we run regression again with the remaining factors, and get the final result.

Figure 2-1. Weekly Data Regression

Company 1 2 3 4 5 6 7

Corn Crude Gold Nikkei S&P 500 Canadian Yen Intercept

ABX US Coefficient 1.465 0.367 -0.566 -0.271 0.000

(P-value) (0.000) (0.000) (0.000) (0.000) (0.715)

XOM US Coefficient 0.662 -0.503 0.001

(P-value) (0.000) (0.000) (0.579)

CAT US Coefficient 0.067 0.029 1.049 -0.466 0.001

(P-value) (0.013) (0.564) (0.000) (0.000) (0.555)

ADM US Coefficient 0.105 0.076 0.690 0.001

(P-value) (0.000) (0.011) (0.000) (0.229)

6301 JP Coefficient 0.985 -0.001 0.176 0.001

(P-value) (0.000) (0.984) (0.014) (0.201)

PORTFOLIO Coefficient 0.035 0.045 0.349 0.219 0.537 -0.274 0.001

(P-value) (0.007) (0.000) (0.000) (0.000) (0.000) (0.000) (0.148)

(Rounded to three decimal places)

3. Hedge strategy based on weekly data.

According to the output above, we analyze the influence of each significant factor. For every stock, we invest five million USD, so the product of five million USD times coefficient is the influence of the factor. Then, dividing the product with the respective latest price, we can get the quantity to sell or buy.

To hedge the risk, we can long or short the underlying assets.The detailed statistics are listed below.

Figure 2-2. Weekly Hedging Strategy

Company Position 1 2 3 4 5 6 7

Corn

(Bushel) Oil

(Gallon) Gold

(Ounce) Nikkei S&P JPY/USD

(in JSY) CAD/USD

(in CAD)

ABX US short 4396.3 1394.2

long 2801161.2 17574.6

XOM US short 2515.7

long 2491564.7

CAT US short 551.4 16.6 3988.0

long 2305293.3

ADM US short 5318.4 227.6 2622.8

long

6301 JP short 561.6 11445.9

long 4.0

PORTFOLIO short 1444.8 11324.3 5232.1 625.6 10204.1

long 6791669.3

(Rounded to one decimal place)

4. Analysis of the weekly data from July 1986 to Dec 1998.

Now, we run the same regressions with the weekly data from July 1986 to Dec 1998.The statistically significant risk factors are showed below.

Figure 3-1. Weekly Data Regression (July 1986- Dec 1998)

Company 1 2 3 4 5 6 7

Corn Crude Gold Nikkei S&P 500 Canadian Yen Intercept

ABX US Coefficient 1.736 0.759 -0.900 -0.333 0.003

(P-value) (0.000) (0.000) (0.001) (0.001) (0.108)

XOM US Coefficient -0.084 0.904 0.000

(P-value) (0.029) (0.000) (0.987)

CAT US Coefficient 1.045 -0.531 -0.001

(P-value) (0.000) (0.019) (0.704)

ADM US Coefficient 0.082 0.129 0.732 0.001

(P-value) (0.000) (0.014) (0.000) (0.398)

6301 JP Coefficient 0.938 0.001

(P-value) (0.000) (0.707)

PORTFOLIO Coefficient 0.034 0.338 0.225 0.647 -0.283 0.001

(P-value) (0.011) (0.000) (0.000) (0.000) (0.005) (0.193)

(Rounded to three decimal places)

The hedge strategies are got in the same way. The detailed statistics are listed below.

Figure 3-2.Weekly Hedging Strategy (July 1986- Dec 1998)

Company Position 1 2 3 4 5 6 7

Corn

(Bushel) Oil

(Gallon) Gold