The £112.6 million fund produced a total return of 29.9% last year on a net asset value basis versus 21% for the FTSE All-World Index.
The trust was helped by a strong position in the Japanese stock market which has long been a barren hunting ground for asset managers but had a good 2013.
Trust chairman Teddy Tulloch said: "Our heavy weighting in Japanese shares was a major factor in the investment performance.
"The Japanese equity market suffered in the aftermath of the tsunami in early 2011. However, our investment manager's conviction about the exceptional value available in many Japanese shares was finally rewarded in 2013."
Dr Nairn increased his weighting by cutting investment in the UK and the rest of Asia in early 2013.
Among his best performers was electronics company Panasonic which in 2012 was forced to take large impairments after being hit by the strong yen. In 2013 its share price rose 124% in local currency terms.
Dr Nairn said: "We consider that it is still not yet expensive."
The trust was also aided by relatively big positions in the US and continental European companies.
Mr Tulloch said: "In the second half of the year, we started to take some profits in Japan as a number of share prices had risen to levels that no longer represented good value.
"The money raised was reinvested in continental Europe where many shares still offered value."
By the year-end 30.9% of the fund was invested in continental European firms and 30.2% in Japan.
Among those holdings cut back or sold were retailer Seven and I and technology company Fujitsu.
Mr Tulloch said: "After such good gains in share prices in the developed markets, many shares are looking expensive and so are vulnerable to profit taking. However, we believe it is still possible to identify shares that represent good long-term value."