How to convert daily returns to annual returns? I have a task: to download daily stock quotations, create a portfolio and draw a CML-line. Risk-free rate was given: 6.5% of annual.
I decided to convert daily returns to annual returns, using formula from here:
$$AnnualReturn = [(DailyReturn + 1)^{365} - 1]*100\%$$
I found out, that result numbers are just insane. For example, for one company price 2017/09/07 was 27.025 , price 2017/09/08 was 27.77. Then
$$ DailyReturn = \frac{27.77-27.025}{27.025} = 0.0276$$
$$AnnualReturn = [(1.0276)^{365} - 1]*100\%=2069063\%$$
I suppose I did something wrong. Could you help me, please?
And there is one more question: can I convert a daily return to annual return like this?
$$AnnualReturn = DailyReturn*365$$
So, let me start with your second question.  No you cannot multiply by 365.  You could approximate it by $$\log(\text{Annual Return})=365*\log(\text{Daily Return}),$$ but for what you are doing, it does not make sense to do so.

You are correct in your annualized rate of return.  It is 2069063%. It should be obvious as to why you would not want to do this.

There are two solutions.  The first is to convert annual rates, such as the bond rate, from an annual format to a daily format.  So make your risk-free rate: $$\text{Daily risk-free rate}=1.065^{\frac{1}{365}}-1=0.0001725485.$$  The second is to search through the dates of your returns and find returns that are 365 days apart, so return would be $$r=\frac{p_{366}}{p_1}.$$

By annualizing daily returns, you are insanely increasing the variability, but it is artificial so it isn't a true increase, it is an artifact of the method you are choosing.