Goetzmann looked at 21 sharemarkets, including New Zealand and Australia, covering the 1900 to 2014 period. His analysis also includes an additional 20 sharemarkets over shorter periods.
His main thesis is that sharemarket bubbles and crashes are rare. He argues there is a large focus on the 1920s Wall Street boom and bust, the 1980s in New Zealand, the 1990s dot-com bubble in the United States and other market crashes, but these are the exception rather than the rule.
He wrote: "I define a bubble as a large price decline after a large price increase or, a crash after a boom. I find that the frequency of bubbles is quite small. The unconditional frequency of bubbles in the data is 0.3 per cent to 1.4 per cent depending on the definition of a bubble.
"Not only are bubbles rare but conditional upon a market boom (ie increasing by 100 per cent in a one or three-year period). Crashes that gave back prior gains happened only 10 per cent of the time. Market prices were more likely to double again following a 100 per cent price boom".
He went on to note: "Most models and analysis of stock market bubbles focuses on a few well-known instances. The overwhelming proportion of price increases in global markets were not followed by crashes. The bubbles that did not burst are just as important for investors to know about as bubbles that did burst".
He concedes that the bigger the boom, the greater the chance of a subsequent decline, but placing a large weight on avoiding bubbles, or misunderstanding the frequency of a crash following a boom, can result in investors missing out on large equity returns.
The Yale professor's analysis is soothing, but market volatility has increased in recent years with the dramatic rise in high-frequency trading and the aggressive role played by hedge funds. In light of this, investors, particularly retirees, should be willing to realise profits given the 100 per cent-plus rise in sharemarkets since 2009.
But the dilemma faced by investors is where to put their money in a low, or even negative, interest rate environment.
The dilemma faced by investors is where to put their money in a low, or even negative, interest rate environment.
A recent Wall Street Journal article reported that Hans Peter Christensen, who lives in Aalborg, Denmark, received a huge surprise when his latest mortgage statement revealed the quarterly interest payment was negative 249 Danish kroner (NZ$55).
Instead of paying interest on his mortgage, the bank paid him the equivalent of $55 in interest for the quarter. As of December 31, his mortgage rate, excluding fees, was negative 0.0562 per cent.
The Association of Danish Mortgage Banks says the country's average short-term mortgage rate is minus 0.09 per cent, compared with minus 0.60 per cent just over a year ago.
The Danish Central Bank doesn't have an inflation target; its goal is to keep the kroner steady with the euro to protect the country's trade with the eurozone. With the euro falling in recent years, the Danish central bank has continued to cut its rates, which went negative for the first time in mid-2012. The Central Bank's certificate of deposit rate now stands at minus 0.65 per cent compared with the country's 0.4 per cent inflation rate.
Christensen, who is a financial consultant, bought his Aalborg house for 1.7 million Danish kroner ($373,600) in 2005. He renegotiated his mortgage as interest rates declined. His mortgage rate dropped below zero in mid-2015, although he still has to make a small payment each quarter because of mortgage fees.
Danish banks no longer pay interest on savings accounts and many Danes - including Christensen - now focus on residential property. Christensen and three other investors bought 10 small apartments for 9.7 million kroner ($2.1 million) with borrowings of 8 million ($1.8 million). The mortgage rate isn't negative but is extremely low.
The low and negative interest rate environment has stimulated the Danish property market, with Copenhagen apartment prices surging 14.5 per cent in 2015, compared with 5.5 per cent the previous year.
Switzerland and Sweden also have negative central bank interest rates - 0.75 per cent and 0.5 per cent respectively - while the European and Japanese central banks currently have rates of 0.0 per cent. This illustrates that central banks are willing to reduce their interest rates to zero or negative in order to raise inflation above its current low levels.
However, these low interest rates encourage borrowing and property speculation. Sweden's central bank governor is concerned that the low and negative interest rates are creating a residential property bubble. The Swedish central bank would like to put some controls on mortgage lending but these powers are in the hands of Sweden's Financial Supervisory Authority, not the central bank.
Swedish house prices have risen 10.8 per cent over the past 12 months, 13.4 per cent in Greater Stockholm. Sweden's inflation rate is 0.8 per cent.
Eric Thedeen, head of the country's Financial Supervisory Authority, said that the central bank's low interest rates - rather than lax regulation - were the primary cause of Sweden's real estate boom. He said: "Low interest rates are a risk because they drive lending and can drive risk taking.
"This is not me criticising the low rates. I am just stating the fact that this is a consequence of central banks stimulating the economy to get inflation up".
Negative interest rates also have an adverse impact on bank profitability and their balance sheet strength. It is very difficult for a bank to make money when it has to pay individuals to borrow, and lodge money at the central bank at negative interest rates.
The New Zealand situation is less dramatic but with an inflation rate of 0.4 per cent, compared with a Reserve Bank target of 1-3 per cent, there is scope for the bank's OCR to go lower than the current 2.25 per cent. As with the Danish central bank, there will be pressure on governor Graeme Wheeler to make further OCR cuts if the New Zealand dollar appreciates against the United States dollar.
Herein lies the dilemma facing investors. New Zealand's largest commercial bank is offering 2.6 per cent for three-month deposits, 3.15 per cent for six months and 3.25 per cent for 12 months. Meanwhile, the New Zealand sharemarket offers an average gross dividend yield of 6.0 per cent, listed property stocks have an average gross yield of nearly 7 per cent and the utilities sector 7.3 per cent.
Sharemarkets have had a good run, but equities - and residential property - continue to be the preferred investment for many investors in the current low interest rate environment.
Further interest rate cuts would continue to make equities and residential property attractive for some investors, particularly on a short-term basis.
Brian Gaynor is an executive director of Milford Asset Management.
