Do Returns for Stocks and Bonds Follow Normal Distributions?

Stock returns following a normal distribution is the foundation of most financial engineering. Opting pricing model, Black–Scholes model, is one example. 

Stock return following a normal distribution makes sense in a way that economic activities affect economic growth in a geometric manner, or a multiplicative manner. In other world 

For example, if I can  invest $100 to buy a factory that can rake in another $100 in a year. The next year I can buy another factory, using the $100 made by the first one. The second year, I can make $200. The third year, I can make $400.

The increase in how much I can make is not linear, it is geometric. By the way, this example also explains what happens behind compound returns.

Stock return following a normal distribution?

Back to how stock returns following a normal distribution. We see from the above example that the increase of how much money I can make doubled every year, which means my value, or stock price, should double every year if PE ration stays the same, right? 

Now let's look at the "double" part. The above example does not account for anything that can happen to how my business. If in the first year. I can  only make $80, $60 or $120. The reinvestment back into my own business could be random.

Then, we say the returns of my business are random and follow a normal distribution. At the same time, by definition stock prices follow a log-normal distribution.

SPY Returns Look Normal (Annual Returns)

What about bonds?

SHY annual Return Distribution

SHY Monthly Return Distribution