Bounty Ended with 50 reputation awarded by noob2
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In my view there isn't a good answer to this question; the daily method introduces autocorrelation between your returns and the yoy samples leave you with little data.

I would let whatever you choose (and I'll mention some of the other things that you could think about below) mainly be guided by what you are trying to achieve with you analysis, e.g. do you care about the mean, standard deviation, worst loss, or still something else? Do you believe that recent returns are more relevant than those from 50 years ago?

So some ideas for what you could do beyond what you mentioned (and depending on your goals these could be reasonable or highly inappropriate):

As hinted at in the comments on the question, for the daily points there are some methods available to adjust e.g. the estimator for the standard deviation of yearly returns to correct for the autocorrelation. So that's one way to go. If there isntisn't an analytical correction, you could come up with one based on simulation from what you consider to be an appropriate idealized distribution.

Another way to go could be bootstrapping. If daily bootstrapping isnt useful for your application, a good trade-off might be to divide your data in weekly or monthly blocks and just sample 52 cq 12 of those.

If you're really interested in the tails, you could also look at something like extreme value theory for estimating returns.

Yet another way to go, if you're interested in crises (as people looking at very long time series often are) could be to model the data as bring emitted from a hidden mark ofMarkov model where markets can be in a few states (e.g. {normal, crisis, recovery}) and estimate return distributions and transition probabilities from them and then sample from you this model.

Yet another alternative could be looking at what distribution fits your daily data well and simulate how that aggregates from daily to yearly for certain percentiles of the distribution.

In my view there isn't a good answer to this question; the daily method introduces autocorrelation between your returns and the yoy samples leave you with little data.

I would let whatever you choose (and I'll mention some of the other things that you could think about below) mainly be guided by what you are trying to achieve with you analysis, e.g. do you care about the mean, standard deviation, worst loss, or still something else? Do you believe that recent returns are more relevant than those from 50 years ago?

So some ideas for what you could do beyond what you mentioned (and depending on your goals these could be reasonable or highly inappropriate):

As hinted at in the comments on the question, for the daily points there are some methods available to adjust e.g. the estimator for the standard deviation of yearly returns to correct for the autocorrelation. So that's one way to go. If there isnt an analytical correction, you could come up with one based on simulation from what you consider to be an appropriate idealized distribution.

Another way to go could be bootstrapping. If daily bootstrapping isnt useful for your application, a good trade-off might be to divide your data in weekly or monthly blocks and just sample 52 cq 12 of those.

If you're really interested in the tails, you could also look at something like extreme value theory for estimating returns.

Yet another way to go, if you're interested in crises (as people looking at very long time series often are) could be to model the data as bring emitted from a hidden mark of model where markets can be in a few states (e.g. {normal, crisis, recovery}) and estimate return distributions and transition probabilities from them and then sample from you this model.

Yet another alternative could be looking at what distribution fits your daily data well and simulate how that aggregates from daily to yearly for certain percentiles of the distribution.

In my view there isn't a good answer to this question; the daily method introduces autocorrelation between your returns and the yoy samples leave you with little data.

I would let whatever you choose (and I'll mention some of the other things that you could think about below) mainly be guided by what you are trying to achieve with you analysis, e.g. do you care about the mean, standard deviation, worst loss, or still something else? Do you believe that recent returns are more relevant than those from 50 years ago?

So some ideas for what you could do beyond what you mentioned (and depending on your goals these could be reasonable or highly inappropriate):

As hinted at in the comments on the question, for the daily points there are some methods available to adjust e.g. the estimator for the standard deviation of yearly returns to correct for the autocorrelation. So that's one way to go. If there isn't an analytical correction, you could come up with one based on simulation from what you consider to be an appropriate idealized distribution.

Another way to go could be bootstrapping. If daily bootstrapping isnt useful for your application, a good trade-off might be to divide your data in weekly or monthly blocks and just sample 52 cq 12 of those.

If you're really interested in the tails, you could also look at something like extreme value theory for estimating returns.

Yet another way to go, if you're interested in crises (as people looking at very long time series often are) could be to model the data as bring emitted from a hidden Markov model where markets can be in a few states (e.g. {normal, crisis, recovery}) and estimate return distributions and transition probabilities from them and then sample from you this model.

Yet another alternative could be looking at what distribution fits your daily data well and simulate how that aggregates from daily to yearly for certain percentiles of the distribution.

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In my view there isn't a good answer to this question; the daily method introduces autocorrelation between your returns and the yoy samples leave you with little data.

I would let whatever you choose (and I'll mention some of the other things that you could think about below) mainly be guided by what you are trying to achieve with you analysis, e.g. do you care about the mean, standard deviation, worst loss, or still something else? Do you believe that recent returns are more relevant than those from 50 years ago?

So some ideas for what you could do beyond what you mentioned (and depending on your goals these could be reasonable or highly inappropriate):

As hinted at in the comments on the question, for the daily points there are some methods available to adjust e.g. the estimator for the standard deviation of yearly returns to correct for the autocorrelation. So that's one way to go. If there isnt an analytical correction, you could come up with one based on simulation from what you consider to be an appropriate idealized distribution.

Another way to go could be bootstrapping. If daily bootstrapping isnt useful for your application, a good trade-off might be to divide your data in weekly or monthly blocks and just sample 52 cq 12 of those.

If you're really interested in the tails, you could also look at something like extreme value theory for estimating returns.

Yet another way to go, if you're interested in crises (as people looking at very long time series often are) could be to model the data as bring emitted from a hidden mark of model where markets can be in a few states (e.g. {normal, crisis, recovery}) and estimate return distributions and transition probabilities from them and then sample from you this model.

Yet another alternative could be looking at what distribution fits your daily data well and simulate how that aggregates from daily to yearly for certain percentiles of the distribution.