Just explicitly reiterate the SUMs (I believe they are only calculated once):
SELECT
business_period,
SUM(transaction.transaction_value) AS total_transaction_value,
SUM(transaction.loss_value) AS total_loss_value,
SUM(transaction.transaction_value) - SUM(transaction.loss_value) AS net_value
FROM transaction
GROUP BY business_period
Alternatively you can use a derived table subquery, which should force it to calculate only once if the above does not do so implicitly - although there may be some additional overhead depending on what the optimizer sees:
SELECT business_period,
total_transaction_value,
total_loss_value,
(total_transaction_value - total_loss_value) AS net_value
FROM
(
SELECT
business_period,
SUM(transaction.transaction_value) AS total_transaction_value,
SUM(transaction.loss_value) AS total_loss_value,
FROM transaction
GROUP BY business_period
) x