In fact, this can be debated. After all, if you would invest in a "total economy basket" (that is, a basket of shares that is an image of the actual economy), then your basket's value will grow with the economic growth. You could think of such a basket as the most possibly hedged fund. There is no lower risk. Even a state bond has a higher risk, and it is considered in the financial world as the risk-less investment reference.
So whether you buy into that "total economy fund" or whether you simply have fixed supply, shouldn't alter anything. At fixed supply, the deflation is (in the long run) equal to the economic growth. If the economy grows with 2% a year, under fixed supply, you can expect a 2% rate deflation. If the economy shrinks with 5%, you can expect, under fixed supply, an inflation of 5%. This is assuming long term stability of the velocity of money.
Now, I don't see the economic utility of investing in a "total economy basket" because it expresses NO PREFERENCE. Now, the value of speculation and investment resides exactly in the CHOICES you make: to support THIS business OVER that business, and hence send a signal to the market. But to send a signal to "the whole of the economy" is equivalent to not sending a signal.
So what can you do ? You can invest specifically. Then you "add value" if you do so in a faster-growing sector, with higher return than the average growth. But you can still do that in a deflationary environment, because investing in a faster-growing sector than the average economy will bring you MORE than the gain by deflation.
If average economic growth is 2% (and hence deflation is 2%) but a certain sector grows at 5% (has a return on investment of 5%), then it would still be beneficial to invest in that sector: you would win 3% in nominal terms (and hence 5% including inflation). You would win over just hoarding.
The only thing is that deflation would evidently make you loose if you invested in sub-optimal sectors, which is less evident to see in an inflationary environment.
So, in the end: in a deflationary environment, hoarding money gives you the average return on your value, in the same way as a useless "full basket" investment would do in a non-deflationary environment. You can still win by investing in a faster-growing sector. However, nobody can win in (over) investing in a lower-return sector, which is possible by a financial sector in an inflationary environment. It is about the sole difference.
But isn't hoarding investing in oneself directly opposite to a total basket? Do both create the same economic environment regardless of inflation/deflation? or is your logic simply based on two negatives ?
Anyway the problem is not *your* wealth, but the economy as a whole. Not the ratios but the absolutes
As a final thought on deflation, Things tend to decay why not money?