In contrast, had the 30 per cent drop in share prices come in the final year they would have had £88,000 left over after 10 years.
Mr Greetham wrote: "The importance of avoiding large losses early on argues against investing the whole pot in company shares as they can see significant year to year swings in price. It also argues against taking excessive risk in the hunt for income."
Rather than investing in either an ultra-low risk way or chasing individual high-risk investments, the author proposed a third way of spreading risk across assets such as company shares, bonds and property, both at home and abroad.
"An active manager can vary the proportions held in each type of investment with the aim of incrementally increasing returns while reducing losses in poor market conditions," he wrote.
Royal London sought to illustrate its theory by examining the behaviour of its £100,000 pension pot in 10,000 scenarios and sticking to a basic set of criteria.
It assumed the pension was invested in one of two multi-asset funds: a defensive fund with 25 per cent of its assets in higher risk, growth-seeking investments and 75 per cent in less volatile sterling bonds and cash and a growth fund with 75 per cent in growth-seeking assets and 25 per cent in bonds and cash.
It looked at two different income requirements: a high income of £7,500 a year, and a more moderate income of £4,500.
It assumed expected returns of 2.5 per cent for the defensive choice with a volatility rate of 4.5 per cent and 4.3 per cent for the growth fund with 10.5 per cent volatility.
For both options fees of 1 per cent were factored in.
Royal London detected poor results when looking at the £7,500 income requirement.
With either fund choice, it found the income level was likely to be sustainable for the first 10 years from retirement, but after that point there were an increasing number of scenarios in which the money ran out.
Returns averaging 2.5 per cent or 4.3 per cent a year were simply not high enough to keep the pension pot topped up with an income of 7.5 per cent of the initial pension pot going out every year, Mr Greetham wrote.
"The fall off was particularly marked for the defensive fund, with the money lasting less than 15 years in more than half of the scenarios (but) the growth fund fared little better," he wrote.
"There were some instances where good returns helped the money to last 20 years or more but the money still ran out in 15 years or less about half of the time."
The research found a £4,500 income requirement to be more sustainable, with the money lasting more than 25 years in more than half of all scenarios tested.
