"This was hardly a one-off, out of character fall from grace by a person who had led an otherwise blameless life," the decision said.
Robertson's lawyer also argued that he should get a "modest" discount on his sentence because of the impact it would have on his 8-year-old son.
"The [High Court] Judge responded to this submission by saying that imprisonment was the inevitable consequence of the decisions Mr Robertson made to offend as he did. No error in this analysis is evident."
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An appeal on the grounds of remorse was also rejected.
"Mr Robertson's very late expression of remorse seems more consistent with his ongoing promotion of self-interest rather than being motivated by any genuine concern for the plight of his victims.
"Mr Robertson undoubtedly now regrets what he did, but this is not the same as genuine remorse."
Further arguments against his sentence were dismissed, including Robertson's claim that he should get more than four months' discount because he helped victims recover some of their money.
The Court of Appeal also backed the decision to impose a minimum period of imprisonment, which can be used if the normal parole period is considered insufficient.
$10m Ponzi scheme
In all, Robertson stole from 22 victims between 2009 and 2015. They were mostly elderly, retired or approaching retirement, and made net losses of around $1.5m.
An unauthorised and unregistered financial adviser, Robertson sold complicated software packages to inexperienced investors, and when they complained about how difficult they were to use he offered to trade their money on their behalf or to sell them shares in his company, Prosper Through Trading (PTT).
"You painted a glowing albeit false picture of your prowess as a trader, for example telling one investor that you were 'as good as John Key'," Judge Sarah Katz said in her sentencing judgement last year.
None of the money was traded, and Robertson instead used it to buy expensive cars, travel by private helicopter, go on luxury weekend getaways or overseas holidays in a private jet, and buy expensive jewellery.
Robertson also operated various companies including PTT Ltd to assist clients to share and trade on the New Zealand and Australian markets.
In essence, however, he was operating what the FMA called a $10m Ponzi scheme.
When low on funds, Robertson also resorted to simply stealing his clients' funds from their credit card accounts without their authority and knowledge.
Justice Katz said the evidence for the charges she found the white collar criminal guilty of was "overwhelming".
She said Robertson was motivated by greed and the appearance of wealth was clearly important to him.
While some of the investors' money was recovered and the prospect of further recovery remains, there was "real likelihood of a large shortfall", Crown prosecutor Ben Finn said.
The court heard Robertson, who has a supportive family, now claims to be remorseful and has accepted some wrongdoing in a letter to his victims.
"I am embarrassed and ashamed in the way I have conducted myself in our dealings," he wrote.
His lawyer, Todd Simmonds, added to that notion and said his client accepted his offending was significant.
While exact figures couldn't be pinpointed, Simmonds said there could be meaningful reparation and recovery for the victims as Robertson's cash and assets - of more than $2 million - are liquidated.
The stories of Robertson's victims made for sad reading, Justice Katz said.
One was now so suspicious of financial people he refuses to deposit his money in a bank, while another man in his 60s has been forced to remortgage his farm.
Most of the 22 victims lost most if not all of their invested money, the judge said in her written reasons for the verdicts, which were provided to the Herald.
The victims, Justice Katz said, were largely elderly, financially naïve, and inexperienced with trading or financial markets.
She said a common theme had developed from the investors' evidence that Robertson "is an extremely skilled salesman, who engendered trust and confidence".
"One complainant described him as being a 'very persuasive sort of a fella ... I reckon he could sell ice to an Eskimo'."
In her nearly 200-page judgment, Justice Katz said Robertson's offers to trade on behalf of investors was "simply a ruse to extract more money from clients".
"He knew that what he was doing was unlawful and set out to create a false paper trail to disguise the reality of what was occurring.
"The investors were generally unperturbed about the precise terms of the documents they signed, but instead relied on their verbal dealings with Mr Robertson.
"They were generally simple, honest, people who had worked hard all their lives and were keen to generate a little extra retirement income from their limited savings. They trusted that Mr Robertson was a man of his word."
One complainant, who worked on a farm all his life, said: "Like you take people on trust, for Christ's sake. Like I can say I sold thousands of tonnes of wheat, over the phone, on a verbal contract. And you take people as it is; I sold the wheat, they put the money in my bank. That's how I operate, on trust."
After Robertson stole his victims' money, he generally distanced himself from the investors and became extremely difficult to contact.
When they did manage to reach him, he would either evade the issue, promise to send an update on their investment - which never arrived - or simply assure them that their investments were doing very well.
On some occasions he would persuade an investor to contribute further funds.
"A particularly unfortunate subset of the VIP or 'trading on behalf' clients were subsequently offered a further 'opportunity' by Mr Robertson," Justice Katz said.
"He invited them to become shareholders in one of his companies, or in a company he claimed that he was planning to set up overseas. A number of investors took up the offer. This group of investors paid tens of thousands of dollars [and in some cases hundreds of thousands of dollars] for fictitious shareholdings."
After sentencing, the FMA's head of enforcement Karen Chang said: "Many people suffered as a result of dealing with Mr Robertson and we strongly condemn what he did.
"We brought this case in part because Mr Robertson was purporting to provide services that would have required him to be an authorised or registered financial adviser. Cases like this can unfairly erode trust in New Zealand's financial advice sector."
Chang also reminded people to always use an FMA-licensed provider.