Question

Suppose that the daily simple returns of a stock in one week were -0.4%, 0.8%, 1.3%, -1.5%, and 0.9%. What are the corresponding daily log returns? What is the weekly simple return of the stock?

Answer 1

		Log returns are continuously compounded return
		Beginning Value of investment =P
		Value at end of period =F
		r=Arithmatic Return =(F/V)-1
		Log Return =LN(F/V)
		Log Return =LN(1+r)
			r	LN(1+r)
			Simple	DailyLog
		DailySimple Return in Percentage	Return	Return
	r1	-0.40%	(0.004)	-0.00401
	r2	0.80%	0.008	0.007968
	r3	1.30%	0.013	0.012916
	r4	-1.50%	(0.015)	-0.01511
	r5	0.90%	0.009	0.00896
		WEEKLY SIMPLE RETURN:R
		1+R=(1+r1)*(1+r2)*(1+r3)*(1+r4)*(1+r5)
		1+R=(1-0.004)*(1+0.008)*(1+0.013)*(1-0.015)*(1+0.009=)	1.0107802
		R=WEEKLY SIMPLE RETURN =1.01078-1=	0.0107802
		WEEKLY SIMPLE RETURN in PERCENTAGE=	1.07802%