Apache Corp. (NYSE:APA)

Capital Asset Pricing Model (CAPM)

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Apache Corp. common stock.

Rates of Return
Variance and Covariance
Systematic Risk (β) Estimation
Expected Rate of Return

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Rates of Return

Apache Corp., monthly rates of return

		Apache Corp. (APA)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_APA,t¹	Dividend_APA,t¹	R_APA,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2011
1.	Feb 28, 2011
2.	Mar 31, 2011
3.	Apr 30, 2011
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2015
59.	Dec 31, 2015
Average (R):
Standard deviation:

		Apache Corp. (APA)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_APA,t¹	Dividend_APA,t¹	R_APA,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2011
1.	Feb 28, 2011
2.	Mar 31, 2011
3.	Apr 30, 2011
4.	May 31, 2011
5.	Jun 30, 2011
6.	Jul 31, 2011
7.	Aug 31, 2011
8.	Sep 30, 2011
9.	Oct 31, 2011
10.	Nov 30, 2011
11.	Dec 31, 2011
12.	Jan 31, 2012
13.	Feb 29, 2012
14.	Mar 31, 2012
15.	Apr 30, 2012
16.	May 31, 2012
17.	Jun 30, 2012
18.	Jul 31, 2012
19.	Aug 31, 2012
20.	Sep 30, 2012
21.	Oct 31, 2012
22.	Nov 30, 2012
23.	Dec 31, 2012
24.	Jan 31, 2013
25.	Feb 28, 2013
26.	Mar 31, 2013
27.	Apr 30, 2013
28.	May 31, 2013
29.	Jun 30, 2013
30.	Jul 31, 2013
31.	Aug 31, 2013
32.	Sep 30, 2013
33.	Oct 31, 2013
34.	Nov 30, 2013
35.	Dec 31, 2013
36.	Jan 31, 2014
37.	Feb 28, 2014
38.	Mar 31, 2014
39.	Apr 30, 2014
40.	May 31, 2014
41.	Jun 30, 2014
42.	Jul 31, 2014
43.	Aug 31, 2014
44.	Sep 30, 2014
45.	Oct 31, 2014
46.	Nov 30, 2014
47.	Dec 31, 2014
48.	Jan 31, 2015
49.	Feb 28, 2015
50.	Mar 31, 2015
51.	Apr 30, 2015
52.	May 31, 2015
53.	Jun 30, 2015
54.	Jul 31, 2015
55.	Aug 31, 2015
56.	Sep 30, 2015
57.	Oct 31, 2015
58.	Nov 30, 2015
59.	Dec 31, 2015
Average (R):
Standard deviation:

Show all

¹ Data in US$ per share of common stock, adjusted for splits and stock dividends.

² Rate of return on common stock of APA during period t

³ Rate of return on S&P 500 (the market portfolio proxy) during period t

Variance and Covariance

Apache Corp., calculation of variance and covariance of returns

t	Date	R_APA,t	R_{S&P 500,t}	(R_APA,t–R_APA)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_APA,t–R_APA)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2011
2.	Mar 31, 2011
3.	Apr 30, 2011
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2015
59.	Dec 31, 2015
Total (Σ):

t	Date	R_APA,t	R_{S&P 500,t}	(R_APA,t–R_APA)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_APA,t–R_APA)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2011
2.	Mar 31, 2011
3.	Apr 30, 2011
4.	May 31, 2011
5.	Jun 30, 2011
6.	Jul 31, 2011
7.	Aug 31, 2011
8.	Sep 30, 2011
9.	Oct 31, 2011
10.	Nov 30, 2011
11.	Dec 31, 2011
12.	Jan 31, 2012
13.	Feb 29, 2012
14.	Mar 31, 2012
15.	Apr 30, 2012
16.	May 31, 2012
17.	Jun 30, 2012
18.	Jul 31, 2012
19.	Aug 31, 2012
20.	Sep 30, 2012
21.	Oct 31, 2012
22.	Nov 30, 2012
23.	Dec 31, 2012
24.	Jan 31, 2013
25.	Feb 28, 2013
26.	Mar 31, 2013
27.	Apr 30, 2013
28.	May 31, 2013
29.	Jun 30, 2013
30.	Jul 31, 2013
31.	Aug 31, 2013
32.	Sep 30, 2013
33.	Oct 31, 2013
34.	Nov 30, 2013
35.	Dec 31, 2013
36.	Jan 31, 2014
37.	Feb 28, 2014
38.	Mar 31, 2014
39.	Apr 30, 2014
40.	May 31, 2014
41.	Jun 30, 2014
42.	Jul 31, 2014
43.	Aug 31, 2014
44.	Sep 30, 2014
45.	Oct 31, 2014
46.	Nov 30, 2014
47.	Dec 31, 2014
48.	Jan 31, 2015
49.	Feb 28, 2015
50.	Mar 31, 2015
51.	Apr 30, 2015
52.	May 31, 2015
53.	Jun 30, 2015
54.	Jul 31, 2015
55.	Aug 31, 2015
56.	Sep 30, 2015
57.	Oct 31, 2015
58.	Nov 30, 2015
59.	Dec 31, 2015
Total (Σ):

Show all

Variance_APA = Σ(R_APA,t–R_APA)² ÷ (59 – 1)
= ÷ (59 – 1)
=

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (59 – 1)
= ÷ (59 – 1)
=

Covariance_{APA, S&P 500} = Σ(R_APA,t–R_APA)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= ÷ (59 – 1)
=

Systematic Risk (β) Estimation

Variance_APA
Variance_{S&P 500}
Covariance_{APA, S&P 500}
Correlation coefficient_{APA, S&P 500}¹
β_APA²
α_APA³

Calculations

¹ Correlation coefficient_{APA, S&P 500}
= Covariance_{APA, S&P 500} ÷ (Standard deviation_APA × Standard deviation_{S&P 500})
= ÷ ( × )
=

² β_APA
= Covariance_{APA, S&P 500} ÷ Variance_{S&P 500}
= ÷
=

³ α_APA
= Average_APA – β_APA × Average_{S&P 500}
= – ×
=

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F
Expected rate of return on market portfolio²	E(R_M)
Systematic risk (β) of Apache Corp. common stock	β_APA

Expected rate of return on Apache Corp. common stock³	E(R_APA)

¹ Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).

² See details »

³ E(R_APA) = R_F + β_APA [E(R_M) – R_F]
= + [ – ]
=

	Apache Corp.	Other companies (not purchased previously)
Financial Statements
Common-Size Financial Statements
Analysis of Financial Ratios
Relative Valuation
Discounted Cash Flow (DCF) Valuation
Long-term Trends
Analysis of Components of Financial Statements
Financial Reporting Quality
Stock Price Trends

	All companies
Financial Statements
Common-Size Financial Statements
Analysis of Financial Ratios
Relative Valuation
Discounted Cash Flow (DCF) Valuation
Long-term Trends
Analysis of Components of Financial Statements
Financial Reporting Quality
Stock Price Trends