Question

You have been given the following return information for a mutual fund, the market index, and the risk-free rate. You also know that the return correlation between the fund and the market is 0.97.

Year	Fund		Market		Risk-Free
2011	–15.20	%	–30.50	%	3	%
2012	25.10		20.10		4
2013	13.00		11.20		2
2014	7.40		8.00		5
2015	–1.56		–3.20		2

Calculate Jensen’s alpha for the fund, as well as its information ratio. (Do not round intermediate calculations. Enter the alpha as a percent rounded to 2 decimal places. Round the ratio to 4 decimal places.)

Answer 1

Year	Fund (F) (%)	Market (M) (%)	Risk Free Return (RF)(%)	[(R)-E(F)]	[(R)-E(F)]^2	[(R)-E(M)]	[(R)-E(M)]^2
2011	-15.20	-30.50	3	-20.9480	438.8187	-31.6200	999.8244
2012	25.10	20.10	4	19.3520	374.4999	18.9800	360.2404
2013	13.00	11.20	2	7.2520	52.5915	10.0800	101.6064
2014	7.40	8.00	5	1.6520	2.7291	6.8800	47.3344
2015	-1.56	-3.20	2	-7.3080	53.4069	-4.3200	18.6624
	28.74	5.60	16.00		922.0461		1527.6680

- Arithmetic Average Return of Fund =

= 5.748%

- Arithmetic Average Return of Stock =

= 1.12%

- Arithmetic Average Return of Stock =

= 3.20%

- Standard Deviation of Fund =

= 13.5797%

- Standard Deviation of Market =

= 17.4795%

- Beta of Fund = Correlation(F,M)*S.D.of Fund*S.D.of market/(S.D.of market)^2

= 0.97*13.5797*17.4795/(17.4795)^2

= 230.2454/305.5336

= 0.7536

Now, Calculating Jensen's Alpha:-

Rf = Average Risk free Return = 3.2%

Rm = Average Market return = 1.12%

RRF = Average Actual Fund Return = 5.748%

So, Jenson's Alpha is 4.1155%

_ Information ratio:-

Year	Fund (F) (%)	Market (M) (%)	Differnce of Returns (D)	[(R)-E(D)]	[(R)-E(D)]^2
2011	-15.20	-30.50	15.30	10.6720	113.8916
2012	25.10	20.10	5.00	0.3720	0.1384
2013	13.00	11.20	1.80	-2.8280	7.9976
2014	7.40	8.00	-0.60	-5.2280	27.3320
2015	-1.56	-3.20	1.64	-2.9880	8.9281
	28.74	5.60	23.14		158.2877

- Arithmetic Average Return of Difference in Return =

= 4.628%

- Standard Deviation of Difference in Return =

= 5.6265%

So, Tracking Error or Standard Deviation of Difference in Return is 5.6265%

Information ratio = (Arithmetic AVerage return of Fund - Arithmetic AVerage return of Market)/Tracking Error

= (5.748%- 1.12%)/5.6265

= 0.8225

So, Information ratio is 0.8225

We were unable to transcribe this image

We were unable to transcribe this image

We were unable to transcribe this image

We were unable to transcribe this image

We were unable to transcribe this image

af = RF - [R: + 3(Rm - R)

We were unable to transcribe this image